case study questions class 9 coordinate geometry

Class 9 Maths Case Study Questions Chapter 3 Coordinate Geometry

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Case study Questions in Class 9 Mathematics Chapter 3  are very important to solve for your exam. Class 9 Maths Chapter 3 Case Study Questions have been prepared for the latest exam pattern. You can check your knowledge by solving  Class 9 Maths Case Study Questions  Chapter 3 Coordinate Geometry

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In CBSE Class 9 Maths Paper, Students will have to answer some questions based on Assertion and Reason. There will be a few questions based on case studies and passage-based as well. In that, a paragraph will be given, and then the MCQ questions based on it will be asked.

Coordinate Geometry Case Study Questions With Answers

Here, we have provided case-based/passage-based questions for Class 9 Maths Chapter 3 Coordinate Geometry

Case Study/Passage-Based Questions

Answer: (d) 2 units

(ii) How far is the library from Shaguns house?

Answer: (b) 2 units

(iii) How far is the library from Alia’s house?

Answer: (d) None of these

(iv) Which of the following is true?

Answer: (b) ABC forms an isosceles triangle

Answer: (d) none of these

(ii) The distance of the bus stand from the house is

Answer: (b) 10 cm

(iii) If the grocery store and electrician’s shop lie on a line, the ratio of the distance of house from grocery store to that from electrician’s shop, is

Answer: (c) 1.2

(iv) The ratio of distances of the house from the bus stand to the food cart is

Answer: (c) 1.1

(v) The coordinates of positions of bus stand, grocery store, food cart, and electrician’s shop form a

Hope the information shed above regarding Case Study and Passage Based Questions for Class 9 Mathematics Chapter 3 Coordinate Geometry with Answers Pdf free download has been useful to an extent. If you have any other queries about CBSE Class 9 Maths Coordinate Geometry Case Study and Passage Based Questions with Answers, feel free to comment below so that we can revert back to us at the earliest possible By Team Study Rate

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Case Study Questions for Class 9 Maths Chapter 3 Coordinate Geometry

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Case Study Questions

Question 1:

Saumya has to reach her office every day at 10:00 am. On the way to her office, she drops her son at school. Now, the location of Saumya’s house, her son’s school and her office are represented by the map below. Using the details given, answer the following questions.

Q1. Find the coordinates of Saumya’s home. (a) (1, 4) (b) (4, 1) (c) (7, 1) (d) (1, 7)

Q2. Find the coordinates of Saumya’s office. (a) (7, 5) (b) (5, 7) (c) (7, 1) (d) (1, 7)

Q3. Find the coordinates of Saumya’s son’s school. (a) (1, 4) (b) (4, 1) (c) (7, 1) (d) (1, 7)

Q4. Find the distance between Saumya’s home and her son’s school. (a) 7km (b) 4km (c) 3km (d) 1km

Q5. Find the distance between Saumya’s office and her son’s school. (a) 7km (b) 4km (c) 3km (d) 1km

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• CBSE Class 9 Mathematics...

CBSE Class 9 Mathematics Case Study Questions

Table of Contents

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If you’re looking for a comprehensive and reliable study resource and case study questions for class 9 CBSE, myCBSEguide is the perfect door to enter. With over 10,000 study notes, solved sample papers and practice questions, it’s got everything you need to ace your exams. Plus, it’s updated regularly to keep you aligned with the latest CBSE syllabus . So why wait? Start your journey to success with myCBSEguide today!

Significance of Mathematics in Class 9

Mathematics is an important subject for students of all ages. It helps students to develop problem-solving and critical-thinking skills, and to think logically and creatively. In addition, mathematics is essential for understanding and using many other subjects, such as science, engineering, and finance.

CBSE Class 9 is an important year for students, as it is the foundation year for the Class 10 board exams. In Class 9, students learn many important concepts in mathematics that will help them to succeed in their board exams and in their future studies. Therefore, it is essential for students to understand and master the concepts taught in Class 9 Mathematics .

Case studies in Class 9 Mathematics

A case study in mathematics is a detailed analysis of a particular mathematical problem or situation. Case studies are often used to examine the relationship between theory and practice, and to explore the connections between different areas of mathematics. Often, a case study will focus on a single problem or situation and will use a variety of methods to examine it. These methods may include algebraic, geometric, and/or statistical analysis.

Example of Case study questions in Class 9 Mathematics

The Central Board of Secondary Education (CBSE) has included case study questions in the Class 9 Mathematics paper. This means that Class 9 Mathematics students will have to solve questions based on real-life scenarios. This is a departure from the usual theoretical questions that are asked in Class 9 Mathematics exams.

The following are some examples of case study questions from Class 9 Mathematics:

Class 9 Mathematics Case study question 1

There is a square park ABCD in the middle of Saket colony in Delhi. Four children Deepak, Ashok, Arjun and Deepa went to play with their balls. The colour of the ball of Ashok, Deepak,  Arjun and Deepa are red, blue, yellow and green respectively. All four children roll their ball from centre point O in the direction of   XOY, X’OY, X’OY’ and XOY’ . Their balls stopped as shown in the above image.

Answer the following questions:

Answer Key:

Class 9 Mathematics Case study question 2

• Now he told Raju to draw another line CD as in the figure
• The teacher told Ajay to mark  ∠ AOD  as 2z
• Suraj was told to mark  ∠ AOC as 4y
• Clive Made and angle  ∠ COE = 60°
• Peter marked  ∠ BOE and  ∠ BOD as y and x respectively

Now answer the following questions:

• 2y + z = 90°
• 2y + z = 180°
• 4y + 2z = 120°
• (a) 2y + z = 90°

Class 9 Mathematics Case study question 3

• (a) 31.6 m²
• (c) 513.3 m³
• (b) 422.4 m²

Class 9 Mathematics Case study question 4

How to Answer Class 9 Mathematics Case study questions

To crack case study questions, Class 9 Mathematics students need to apply their mathematical knowledge to real-life situations. They should first read the question carefully and identify the key information. They should then identify the relevant mathematical concepts that can be applied to solve the question. Once they have done this, they can start solving the Class 9 Mathematics case study question.

Students need to be careful while solving the Class 9 Mathematics case study questions. They should not make any assumptions and should always check their answers. If they are stuck on a question, they should take a break and come back to it later. With some practice, the Class 9 Mathematics students will be able to crack case study questions with ease.

Class 9 Mathematics Curriculum at Glance

At the secondary level, the curriculum focuses on improving students’ ability to use Mathematics to solve real-world problems and to study the subject as a separate discipline. Students are expected to learn how to solve issues using algebraic approaches and how to apply their understanding of simple trigonometry to height and distance problems. Experimenting with numbers and geometric forms, making hypotheses, and validating them with more observations are all part of Math learning at this level.

The suggested curriculum covers number systems, algebra, geometry, trigonometry, mensuration, statistics, graphing, and coordinate geometry, among other topics. Math should be taught through activities that include the use of concrete materials, models, patterns, charts, photographs, posters, and other visual aids.

CBSE Class 9 Mathematics (Code No. 041)

Class 9 Mathematics question paper design

The CBSE Class 9 mathematics question paper design is intended to measure students’ grasp of the subject’s fundamental ideas. The paper will put their problem-solving and analytical skills to the test. Class 9 mathematics students are advised to go through the question paper pattern thoroughly before they start preparing for their examinations. This will help them understand the paper better and enable them to score maximum marks. Refer to the given Class 9 Mathematics question paper design.

QUESTION PAPER DESIGN (CLASS 9 MATHEMATICS)

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Class 9 is an important milestone in a student’s life. It is the last year of high school and the last chance to score well in the CBSE board exams. myCBSEguide is the perfect platform for students to get started on their preparations for Class 9 Mathematics. myCBSEguide provides comprehensive study material for all subjects, including practice questions, sample papers, case study questions and mock tests. It also offers tips and tricks on how to score well in exams. myCBSEguide is the perfect door to enter for class 9 CBSE preparations.

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14 thoughts on “CBSE Class 9 Mathematics Case Study Questions”

This method is not easy for me

aarti and rashika are two classmates. due to exams approaching in some days both decided to study together. during revision hour both find difficulties and they solved each other’s problems. aarti explains simplification of 2+ ?2 by rationalising the denominator and rashika explains 4+ ?2 simplification of (v10-?5)(v10+ ?5) by using the identity (a – b)(a+b). based on above information, answer the following questions: 1) what is the rationalising factor of the denominator of 2+ ?2 a) 2-?2 b) 2?2 c) 2+ ?2 by rationalising the denominator of aarti got the answer d) a) 4+3?2 b) 3+?2 c) 3-?2 4+ ?2 2+ ?2 d) 2-?3 the identity applied to solve (?10-?5) (v10+ ?5) is a) (a+b)(a – b) = (a – b)² c) (a – b)(a+b) = a² – b² d) (a-b)(a+b)=2(a² + b²) ii) b) (a+b)(a – b) = (a + b

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Class 9th Maths - Coordinate Geometry Case Study Questions and Answers 2022 - 2023

Class 9th Maths - Coordinate Geometry Case Study Questions and Answers 2022 - 2023 Study Materials Sep-08 , 2022

QB365 provides a detailed and simple solution for every Possible Case Study Questions in Class 9th Maths Subject - Coordinate Geometry, CBSE. It will help Students to get more practice questions, Students can Practice these question papers in addition to score best marks.

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QB365 - Question Bank Software

Coordinate geometry case study questions with answer key.

Final Semester - June 2015

(b) What are the coordinates of C and D respectively?

(c) What is the distance between B and D?

(d) What is the distance between A and C?

(e) What are the coordinates of the point of intersection of AC and BD?

(ii) What are the coordinates of Police Station?

(iii) Distance between school and police station:

(iv) What are the coordinates of Library?

(v) In which quadrant the point (-1, 4) lies?  

(b) What are the coordinates of A and B respectively?

(c) The coordinates of point O in the sketch -2 is

(d) The point on the y-axis ( in sketch 2) which is equidistant from the points B and C is 

(e) The point on the x-axis ( in sketch 2) which is equidistant from the points C and D is

(b) What are the coordinates of R, taking A as origin?

(c) Side of lawn is :

(d) Shape of lawn is :

(e) Area of lawn is :

(ii) What are the coordinates of position 'D'?

(iii) What are the coordinates of position 'H'?

(iv) In which quadrant, the point 'C' lie?

(v) Find the perpendicular distance of the point E from the y-axis.

*****************************************

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• Important Questions for CBSE Class 9 Maths Chapter 3 - Coordinate Geometry

Download Important Questions for Class 9 Maths Chapter 3 - Coordinate Geometry - Free PDF

Welcome to our comprehensive collection of Important Questions for CBSE Class 9 Maths Chapter 3 - Coordinate Geometry available in Vedantu. As students progress through their academic journey, mastering the concepts of Coordinate Geometry becomes essential. Our carefully curated list of questions aims to provide students with a thorough understanding of this chapter and boost their problem-solving skills. With a focus on CBSE guidelines and exam patterns, these questions cover various topics such as plotting points, finding distances, and calculating gradients on the coordinate plane. Whether you're looking to strengthen your knowledge or preparing for exams, our curated set of important questions is a valuable resource to excel in Coordinate Geometry. Get ready to explore the fascinating world of coordinates and elevate your mathematical prowess!

Download CBSE Class 9 Maths Important Questions 2024-25 PDF

Also, check CBSE Class 9 Maths Important Questions for other chapters:

Study Important Questions for Class - 9 Mathematics Chapter – 3 Coordinate Geometry

Section - A

1 On which axes do the given points lie?

ii. (0, -3)

iii. (0, 6)

iv. (-5, 0)

i. (7,0) X-axis since the y component is zero

ii. (0, -3) Y-axis since the x component is zero

iii. (0,6) Y-axis since the x component is zero

iv. (-5,0) X-axis since the y component is zero

2 In which quadrants do the given points lie?

ii. (-3, 7)

iii. (-1, -2)

iv. (3, 6) 

i. (4,-2) IV quadrant since the x component is positive and y component is negative

ii. (-3,7) II quadrant since the x component is negative and y component is positive

iii. (-1,-2) III quadrant since the x component is negative and y component is negative

iv. (3,6) I quadrant. since the x component is positive and y component is positive

3. Do P (3, 2) & Q(2, 3) represent the same point? 

Ans: P(3,2) and Q(2,3) do not represent the same point. The first one has the x component is 3 and y is two, while Q has the x component as 2 and y component is 3.

4. In which quadrant points P(3,0), Q(6,0) , R (-7.0), S (0,-6), lie?

Ans: These points do not lie in any quadrant. These points lie on the axes.

5. If a<0 and b<0, then the point P(a,b) lies in

a) quadrant IV

b) quadrant II

c) quadrant III

d) quadrant I

Ans: (c) quadrant III

6. The points (other than the origin) for which the abscissa is equal to the ordinate lie in

a) Quadrant I only

b) Quadrant I and II

c) Quadrant I & III

d) Quadrant II only.

Ans: (c) quadrant I & III. 

In III and I quadrants, the axes have the same sign.

7. The perpendicular distance of the point P(4,3) from the y axis is

c) 7 Units 

Ans: (a) 3 units

Distance from the Y axis is the x coordinate of the point.

8. The area of triangle OAB with 0(0,0), A(4,0) & B(0,6) is

a) 8 sq. unit

b) 12 sq. units

c) 16 sq. units

d) 24 sq. units

Ans: (b) 12 sq. units.

Area is half of the product of base and height of the triangle.

Section - B

9. Write down the coordinates of each of the points P, Q, R, S and T as shown in the following figure?

10. Draw the lines X'OX and YOY as the axes on the plane of a paper and plot the given points.

ii. B (-3, 2)

iii.  C(-5, -4)

iv. D(2,-6) 

Section - C

11. Find the mirror images of the following point using x-axis & y-axis as mirror.

ii.  B(2,-3)

iii. C(-2,3)

iv. D(-2,-3)

Ans:  

i. A’ (2,-3),

ii. B’ (2,3)

iii. C’ (-2,-3), 

iv. D’ (-2,3)

12. Draw the graph of the following equations

i. \[{\bf{y}} = {\bf{3x}} + {\bf{2}}\]

ii. \[{\bf{y}} = {\bf{x}}\]

13. Draw a triangle with vertices 0(0,0) A(3,0) B(3,4). Classify the triangle and also find its area.

Ans:   The points from a right angle triangle

The area of the triangle is half of the product of the base and height i.e. 6 square units.

14. Draw a quadrilateral with vertices A(2,2) B(2,-2) C(-2,-2), D(-2,2). Classify the quadrilateral and also find its area.

This quadrilateral is square of area =16 square units.

15. Find the coordinates of point which are equidistant from these two points P(3,0) and Q(-3,0). How many points are possible satisfying this condition?

Ans: All the point on the Y-axis satisfy this condition.

1 Mark Questions

1. The point of intersection of X and Y axes is called

(a) zero point

(c) null point

(d) none of these 

Ans: (b) origin

2. The distance of the point (-3, -2) from x-axis is

(a) 2 units

(b) 3 units

(c) 5 units

(d) 13 units 

Ans: (a) 2 units

Distance from the x axis is the magnitude/absolute value of the y coordinate of the point.

3. The distance of the point (-6, -2) from y-axis is

(a) 6 units

(b) 10 units

(c) 2 units

(d) 8 units 

Ans : (a) 6 units

Distance from the y axis is the magnitude/absolute value of the x coordinate of the point.

4. The abscissa and ordinate of the point with Co-ordinates (8, 12) is

(a) abscissa 12 and ordinate 8

(b) abscissa 8 and ordinate 12

(c) abscissa 0 and ordinate 20

(d) none of these

Ans: (a) abscissa 12 and ordinate 8

Abscissa is the y coordinate of the point and the ordinate is the x coordinate value.

5. The co-ordinate of origin in

(b) (0, y) 

(d) none of these.

Ans : (c) (0, 0)

For the origin, both abscissa and ordinate are 0.

6. The distance of the point (2,3) from y axis’s

(A) 2 units

(B) 3 units

(C) 5 units

(D) 13 units 

Ans: (A) 2 units

Distance from the x axis is the magnitude/absolute value of the y coordinate of the point. And the distance from the y axis is the magnitude/absolute value of the x coordinate of the point.

7. The point (-2, -1) lies in

(A) 1st quadrant

(B) 2nd quadrant

(C) 3rd quadrant

(D) 4th quadrant

Ans: (C) 3rd quadrant

3 rd quadrant corresponds to both negative x and y values.

8. The point (3,0) lies on

(A) +ve x axis

(B) – ve x axis

(C) + ve y axis

(D) –ve y axis 

Ans: (A) +ve x axis

Since the y coordinate is zero and x-coordinate is positive.

9. The distance of the point (3, 5) from x- axis is

(a) 3 units

(b) 4 units

(d) 6 units  

Ans: (c) 5 units

10. The point (0, -5) lies on

(a) +ve x- axis

(b) +ve y- axis

(c) –ve x- axis

(d) –ve y-axis 

Ans: (d) –ve y-axis

Since the x-coordinate is zero and y is negative.

11. The point (-2, 5) lies in

(a) 1st quadrant

(b) 2nd quadrant

(c) 3rd quadrant

(d) 4th quadrant

Ans: (b) 2nd quadrant.

In the second quadrant, the x-values are negative and y are positive.

12. The distance of the point (3, 0) from x- axis is

(b) 0 units

(c) 9 units

Ans: (a) 3 units.

2 Marks Questions

1. Write the name of each part of the plane formed by Vertical and horizontal lines.

Ans: Vertical line is called y-axis, the horizontal line is called x-axis. And these form four quadrants.

2. Write the Co-ordinates of a point which lies on the x-axis and is at a distance of 4units to the right of origin. Draw its graph.

Ans: (4, 0)

3. Write the mirror image of the point (2, 3) and (-4, -6) with respect to x-axis.

Ans: The mirror image of point (2, 3) is (2, -3) with respect to x-axis.

The mirror image of (-4, -6) is (-4,6) with respect to the x-axis.

4. Write the Coordinates of a point which lies on the y-axis and is at a distance of 3 units above x-axis. Represent on the graph.

Ans: The Coordinates of the point which lies on y-axis and at a distance of 3units above x- axis is (0, 3).

5. Write abscissa and ordinate of point (-3, -4) 

Ans: Abscissa -3 ordinate -4

6. State the quadrant in which each of the following points lie: 

(ii) (-7,11)

(iii) (-6, -4) 

(iv) (-5, -5)

Ans: (2, 1) I Quadrant

(-7, 11) II Quadrant

(-6, -4) III Quadrant

(-5, -5) III Quadrant

7. Which of the following points belongs to 2nd quadrant

(ii) (-3,2)

(iii) (2,0)

(iv)  (-4,2)

Ans: The points (-3, 2), (-4, 2) belong to the 2nd quadrant.

8. What is the name of horizontal and vertical lines drawn to determine the position of any point in the Cartesian plane?

Ans: The horizontal line is called x –axis and the name of vertical line is y – axis

9. Name the points of the plane which do not belong to any of the quadrants.

Ans: The points in a plane which do not belong to any one of the quadrants is origin which is denoted by O (0,0).

10. Which of the following points belong to the x- axis? 

(a) (2, 0) (b) (3, 3) (c) (0, 1) (d) (-2, 0)

Ans: (2, 0) and (-2, 0) belong to the x- axis.

To belong on the y axis the y-component should be zero.

11. Which of the following points belongs to 1st quadrant 

(a) (3, 0) (b) (1, 2) (c) (-3, 4) (d) (3, 4)

Ans: (1, 2) and (3, 4) belong to the 1st quadrant.

12. Which of the following points belongs to 3rd quadrant

(a) (1, 3) (b) (-1, -3) (c) (0, 4) (d) (-4, -2)

Ans: (-1, -3) and (-4, -2) belong to the 3rd quadrant.

3 Marks Questions

1. How will you describe the position of a table lamp on your study table to another person?

Consider the figure of a tabletop, on which a lamp (L)  is placed.

Consider the lamp on the table as a point and the table as a plane. 

Choose one of the corners as the Origin-O (0,0). Measure the distance of the lamp from the shorter edge and the longer edge. Let us assume that the distance of the lamp from the shorter edge is 3m and from the longer edge, its 2m.

Therefore, we can conclude that the position of the lamp on the table can be described in two ways depending on the order of the axes as (3,2).

2. Write the answer of each of the following questions:

(i) What is the name of horizontal and the vertical lines drawn to determine the position of any point in the Cartesian plane?

Ans: The horizontal line that is drawn to determine the position of any point in the Cartesian plane is named the x-axis and the vertical line is called the y-axis.

(ii) What is the name of each part of the plane formed by these two lines?

Ans: The name of each part of the plane that is formed by x-axis and y-axis is called a quadrant.

(iii) Write the name of the point where these two lines intersect.

Ans: The point, where the x-axis and the y-axis intersect is called the origin denoted by O(0,0).

3. In which quadrant or on which axis do each of the points (– 2, 4),  (3, – 1),  (-1,0), (1,2) and (–3,–5) lie? Verify your answer by locating them on the Cartesian plane.

Ans: Tpoint (– 2, 4) lies in II quadrant;

the point (3, – 1) lies in IV quadrant;

the point (– 2, 4) lies in II quadrant; 

the point (3, – 1) lies in IV quadrant and  

the point (–1, 0) lies on the x-axis.

These can be verified from the figure below.

4. Plot the points (x, y) given in the following table on the plane, choosing suitable units of distance on the axes.

5. Locate the points (5, 0), (0, 5), (2, 5), (5, 2), (-3, 5), (-3, -5) and (6, 1) in the Cartesian plane.

6. Take a triangle ABC with A (3, 0), B (-2, 1), C (2, 1). Find its mirror image.

Ans: Mirror images of A (3, 0), B (-2, 1) and C (2, 1) about the x-axis are A’ (3, 0),  B’(-2,-1),  C’(2,-1) respectively. 

7. In fig. write the Co-ordinates of the points and if we join the points write the name of fig. formed. Also write Co-ordinate of intersection point of AC and BD. 

(i) The Co-ordinate of point A is (0, 2), B is (2, 0), C is (0, -2) and D is (-2,0).

(ii) It we joined them we get square.

(iii) Co-ordinate of intersection point of AC and BD is (0, 0).

8. In which quadrant or on which axis do each of the points (-2, 4), (2, -1), (-1, 0), (1, 2) and (-3, -5) lie? Verify your answer by locating them on the Cartesian plane.

(-2, 4) lies in II quadrant;

(2, -1) lies in IV quadrant;

(-1, 0) lies on –ve x-axis;

(1, 2) lies in I quadrant and

(-3, -5) lies in III quadrant.

This can be verified using the following graph: 

9. In fig of vertices find co-ordinates of triangle ABC

Ans: (A) (0, 0) (B) (2, 3) (c) (-2, 3)

10. Take a quadrilateral ABCD

(A) (-5, -4) (B) (-5, 2) (C) (-3, 3) and (D) (-3, 4) find its mirror image with respect to y- axis.

Ans: The mirror image of point.

(A) (-5, 4) (B) (-5, 2) (C) (-3, 3) and (D) (-3, 4) wrt y-axis are.

A’ (5, 4), B’ (5, 2), C’ (3, 3) and D’ (3, 4)

11. Locate the points (A) (-3, 4) (B) (3, 4) and (C) (0, 0) in a Cartesian plane write the name of figure which is formed by joining them.

The figure formed is a triangle.

12. Find Co-ordinates of vertices of rectangle ABCD

Ans: The co- ordinates of vertices of rectangle A (2, 2), B (-2, 2), C (-2, -2) and D (2, -2).

13. Take a rectangle ABCD with A (-6, 4), B (-6, 2), C (-2, 2) and D (-2, 4). Find its mirror image with respect to x- axis.

Ans: The mirror image of A (-6, 4) is A’ (-6, -4) and B (-6, 2) is B’ (-6, -2), C (-2, 2) is C’ (-2, -2) and D (-2, 4) is D’ (-2, -4)

14. The following table gives measures (in degrees) of two acute angles of a right triangle

Plot the point and join them.

15. Plot each of the following points in the Cartesian Plane 

(b) (-3, -4)

(c) (0, -5)

(d) (2, -5)

(e) (2, 0) 

4 Marks Questions

1. (Street Plan): A city has two main roads which cross each other at the centre of the city. These two roads are along the North-South direction and East-West direction.

All the other streets of the city run parallel to these roads and are 200 m apart. There are 5 streets in each direction. Using 1cm = 200 m, draw a model of the city on your notebook. Represent the roads/streets by single lines. There are many cross- streets in your model. A particular cross-street is made by two streets, one running in the North - South direction and another in the East – West direction. Each cross street is referred to in the following manner: If the 2nd street running in the North - South direction and 5th in the East - West direction meet at some crossing, then we will call this cross-street (2, 5). Using this convention, find:

(i) how many cross - streets can be referred to as (4, 3).

(ii) how many cross - streets can be referred to as (3, 4).

Ans: We need to draw two perpendicular lines as the two main roads of the city that cross each other at the center and let us mark it as N-S and E-W.

Let us take the scale as 1 cm = 200m.

Following figure shows the perpendicular roads .

(i) From the figure it can be inferred that only one point have the coordinates as (4,3). Hence, it can  be concluded that only one cross - street can be referred to as (4, 3).

(ii) Only one point have the coordinates as (3,4). Therefore, it can be concluded that only one cross - street can be referred to as (3, 4).

2. See Fig.3.14, and write the following:  

(i) The coordinates of B. 

Ans: The coordinates of point B in the above figure is the distance of point B from x-axis and y- axis. Therefore, we can conclude that the coordinates of point B are (―5, 2).

(ii) The coordinates of C.

Ans: The coordinates of point C in the above figure is the distance of point C from x-axis and y- axis. Therefore, we can conclude that the coordinates of point C are (5, ―5).

(iii) The point identified by the coordinates (–3, –5).

Ans: The point E represents the coordinates (―3, ―5).

(iv) The point identified by the coordinates (2, – 4). 

Ans: The point G that represents the coordinates (2, ―4).

(v) The abscissa of the point D. 

Ans: The abscissa of point D in the given figure is the distance of point D from the y-axis which is 6.

(vi) The ordinate of the point H. 

Ans: The ordinate of point H in the above figure is the distance of point H from the x-axis which is ―3.

(vii) The coordinates of the point L. 

Ans: The coordinates of point L in the above figure is the distance of point L from x-axis and y-axis. Therefore, we can conclude that the coordinates of point L are (0, 5).

(viii) The coordinates of the point M.

Ans: The coordinates of point M in the above figure is the distance of point M from x-axis and y-axis. Therefore, we can conclude that the coordinates of point M are (―3, 0).

5 Marks Questions

1. See fig. and write the following

(i) The Co-ordinates of B

Ans: (-5,2) 

(ii) The Co-ordinates of C

Ans: (5, -5)

(iii) On which axis point L lies.

Ans: Y-axis

(iv) The abscissa of the point D  

Ans: As shown in the figure the abscissa of point D is 6.

(v) The Co-ordinates of point L

Ans: (0, 5)

(vi) On which axis point M lies. 

Ans: Point M lies on X-axis.

(vii) The ordinate of the point H

Ans: The ordinate of point H is -3

(viii) The Co-ordinates of the point M

Ans: (-3, 0)

(ix) The point identified by the Co-ordinate (2, -4)

Ans: G has the coordinate (2,-4)

(x) The point identified by the Co-ordinates (-3, -5)

Ans: E has the coordinate (-3,-5)

2. Find some ordered pairs of the linear equation \[{\bf{2x}} + {\bf{y}} = {\bf{4}}\] and plot them ‘how many such ordered pairs can be found and plotted?

Ans: The given equation is \[2x + y = 4\] The equation holds if

\[x = 0,\,y = 4\] i.e. (0, 4),

\[x = 1,\,y = 2\] i.e. (1, 2),

\[x = 2,\,y = 0\] i.e. (2, 0) ,

\[x = 3,\,y =  - 2\] i.e. (3, -2)…

Similarly (4,-4), (5,-6), (-1,6), (-2,8) etc. also. These are a few ordered pares which are valid solutions. And there are infinite such ordered pairs

3. The following table given the relation between natural numbers and odd natural numbers

Plot the points and join them. Do you get a straight line by joining these points?

Yes a straight line is obtained by joining these points.

Chapter 3 Maths Class 9 Important Questions - Free PDF Download

The Coordinate Geometry Class 9 Important Questions present reliable and accurate learning elements for students to understand the chapter efficiently. The students will receive the necessary understanding of the chapters to clear the difficult problems in class. Expert subject teachers of mathematics prepare these questions. Hence, solving these questions will help students obtain a better understanding of the type of questions asked in the examinations and how to format their answers correctly.

Vedantu presents a free PDF to download for Class 9 Chapter 3 Important Questions so that students can prepare well according to the CBSE syllabus. Students need to understand these guidelines and find solutions with a proper explanation. This free PDF online will surely help students understand their concepts and build a solid base on Coordinate Geometry.

Important Questions for Class 9 Maths Coordinate Geometry

Coordinate geometry is an intriguing subject where students get to learn about the object’s position in a plane, learn about the concepts and coordinates of the cartesian plane and so on. The topics covered in the chapter are : 

Introduction 

Cartesian System 

Plotting a Point 

Coordinate geometry.

Coordinate geometry deals with the locating points on a plane when the aligned numbers, called coordinates for a particular point, are given. It presents geometric aspects in Algebra and allows them to solve geometric problems.

Concepts of Coordinates

The intersection point of the x-axis and the y-axis is identified as the origin. Both x and y are 0 at this point.

The right-hand side of the x-axis values are positive, and the x-axis values on the left-hand side are negative.

Similarly, the values located above the origin on the y-axis, are positive, and the values are negative, which are located below the origin.

It is determined by a collection of two numbers, to locate a point on the plane. 

Cartesian System

A Cartesian coordinate system is a system in two dimensions that can be used to locate a  point with the help of two unique numbers called coordinates. The point along the x-axis is called the x-coordinate and the point along the y-axis is called the y-coordinate.

Two perpendicular directed lines are stipulated to define the coordinates, and the unit length is marked off on the two axes (fig 1). Cartesian coordinate systems are also used in higher space dimensions. 

By using the Cartesian coordinate system, geometric shapes are represented by algebraic equations. For example, radius 2 circle may be defined by the equation x² + y² = 4 (Figure 2).

Distance Between Two Points

Distance between two points of the plane

(x₁, y₁) and (x₂, y₂) is d = [(x₂ – x₁)² + (y₂ – y₁)]¹/²

In case of a three-dimensional system, the formula of the distance between the points 

(x₁, y₁, z₁) and (x₂, y₂, z₂) is d = [(x₂ – x₁)² + (y₂ – y₁)² + (z₂ – z₁)² ] 1/2

Vector Representation

The two-dimensions vector, from the origin to the point with the cartesian coordinates (x, y) can be written as r = xi + yj where i = (1,0) and j = (0,1) are vectors units in the direction of the x-axis and y-axis respectively.

In three-dimensions cases, we will have r = xi + yj + zk, where k = (0,0,1) is the vector unit in the direction of z-axis.

To plot or graph points, we can employ two perpendicular lines called the x-axis and the y-axes. The x-axis is horizontal, and the y axis is the vertical line. The part of the x-axis towards the right of origin is the positive x-axis, and the one towards the left of the origin is the negative x-axis. Similarly, the part of the y-axis above the origin is the positive y-axis, and the part of y-axis below the origin is the negative y-axis. In the coordinate plane, every point is designed by an assigned pair of x and y coordinates.

Let's Consider the Example

Using the Pencil, Plot the Point −4,3

The first coordinates inform about the right or left movement from the origin. The second coordinate tells about the up or down movement from the origin.

Since x coordinate is a −4, there is a movement towards the left 4 units from the origin. The coordinate of y is 3, which means movement two units vertically up to get to the point −4,3. 

List of Important Questions for Class 9 Maths Chapter 3

Chapter 3 Maths Class 9 Important Questions include different types of questions that cover all the sub-topics of the entire chapter. Important questions from each topic are covered in the PDF to provide students with a clear and logical understanding of the chapter. Some of the important questions that are frequently asked in the exam from this chapter are-

In which axis or quadrant do each of the points (–2, 4), (3, –1), (–1, 0),(1, 2) and (–3, –5) lie? Prove your answer by placing them on the Cartesian plane.

Plot the points (y, z) in the following table on the plane, picking proper units of distance on the axes where 

State the name of the point where two lines intersect.

Define the three-dimensional Cartesian coordinate system.

Locate the points in the Cartesian plane (0, 5), (5, 0), (2, 5), (–3, 5), (5, 2),(–3, –5), (5, –3) and (6, 1). 

State the name of vertical lines and the horizontal lines formed to determine the position of any point in the Cartesian plane? 

State the name of every part of the plane developed by two lines?

Describe the Cartesian plane.

Two rolling dice are rolled at the same time. Let the numbers on Dice1 and Dice 2 be denoted by y and z respectively. After each roll, the point S(y, z) is outlined in the plane. Plot all the probable positions of S, and highlight those positions for which the sum of y and z is 8.

In the Cartesian plane plot the five points for which ordinate and the abscissa are equal.

In the Cartesian plane plot the following points - A (1.3, 2.4), B ( - 2.7, 3.2), C ( - 1.1,  - 3.6) and D (4, - 2)

Practice Questions from Class 9 Chapter 3 Maths Coordinate Geometry

1. Find the distance of the point (-3, 4) from the x-axis. 

2. If the points A(x, 2), B(-3, 4) and C(7, -5) are collinear, then find the value of x.

3. For what value of k will k + 9, 2k – 1 and 2k + 7 be the consecutive terms of an A.P.?

4. Find the relation between x and y if the points A(x, y), B(-5, 7) and C(-4, 5) are collinear.

5. Find the ratio in which the y-axis divides the line segment joining the points A(5, -6) and B(-1, -4). Also, find the coordinates of the point of division.

6. Let P and Q be the points of trisection of the line segment joining the points A (2, -2) and B (-7, 4) such that P is nearer to A. Find the coordinates of P.

Benefits of Chapter 3 Maths Class 9 Important Questions

The Basic Concepts of Coordinate Geometry assists students in achieving a high grade by providing a thorough comprehension of the chapter's principles. Pupils that understand the ideas, theories, and calculations can achieve higher percentages on their exams. The following are some of the advantages of significant problems for class 9 mathematics coordinate geometry:

The Coordinate Geometry Class 9 Important Questions PDF is prepared according to the examination guidelines to help students score well in the examinations.

Expert Mathematics subject teachers prepare these questions.

The questions are prepared after a thorough analysis of the previous year's question papers combining the syllabus’s revisions.

The PDF also comprises solutions so that students can refer to them in case of any doubts.

Students can check information about the topics by following the reference books or by searching them on the Vedantu portal.

Practising questions from the PDF will develop the student’s understanding of the concepts and the examination pattern.

Key Features of Important Questions Class 9 Maths Chapter 3 - Coordinate Geometry

All the questions are written from an examination point of view.

Step-by-step solutions for questions with accurate explanations.

The solutions are clear and easy to understand.

Learning is quick as they are clearly written by subject experts to match the curriculum.

These important questions help in developing a good conceptual foundation for students.

These solutions are absolutely free and available in PDF format.

Conclusion 

Crucial Questions for Class 9 Mathematics Coordinate Geometry are essential and reputable sources of study material created for pupils in a well-structured and readily comprehensible style. It will assist pupils in properly comprehending the chapters. The pupils will get the understanding of the chapters required to solve the challenging issues in class. The crucial questions will assist students in covering all of the issues and scoring high marks.

FAQs on Important Questions for CBSE Class 9 Maths Chapter 3 - Coordinate Geometry

1. Which chapter is the most important in Class 9 Maths?

Chapter 3 of Class 9 Maths is about geometry which is the branch of Mathematics concerned with spatial connections among diverse things, individual object forms, and surrounding space characteristics. Class 9 is an important year for high school students since it is during this year that students lay the groundwork for all of the major topics and ideas covered in the Class 10 Board examinations. Students will learn how to identify points in a cartesian system or an XY plane in the chapter Coordinate Geometry. This notion is critical for determining the position of an object in a certain location.

2. How can I practise Chapter 3 of Class 9 Maths?

Geometry is the component of Mathematics that demands a comprehension of the topic as well as certain visualising abilities that students should work on to improve. Vedantu's Crucial Questions for Class 9 Mathematics Coordinate Geometry are valuable and trustworthy sources of study material supplied for students in a well-structured and easily understandable format. These vital questions are available for free on Vedantu (vedantu.com) and its mobile app. It will help pupils understand the chapters thoroughly. Students will get a grasp of the chapters needed to answer the difficult problems in class. The essential questions will help pupils cover all of the issues and achieve good grades.

3. What are case study questions in Class 9 Maths?

Case study questions in Class 9 Maths are the questions that introduce a particular scenario and its mathematical aspect and then proceeds to ask some questions that are relevant to the given chapter i.e. Coordinate Geometry in this case. Case study questions usually involve a real life-based situation where the questions check the students’ analytical ability to follow through and subsequently apply the Maths to it. They are extremely important as they carry a lot of marks and are really simple to get through.

4. How to plot a point?

To plot or graph points, we can use two perpendicular lines known as the x- and y-axes. The horizontal x-axis is parallel to the vertical y-axis. The positive x-axis is located to the right of the origin, while the negative x-axis is located to the left of the origin. Likewise, the positive y-axis is the part of the y-axis above the origin, and the negative y-axis is the part of the y-axis below the origin. Every point in the coordinate plane is defined by a given pair of x and y coordinates.

5. What is coordinate geometry?

Coordinate geometry is concerned with identifying points on a plane when the aligned values, known as coordinates for a certain point, are supplied. It introduces geometric concepts in Algebra and helps students to solve geometric problems. The origin is defined as the point at where the x-axis and y-axis connect. At this moment, both x and y are zero. To identify a point on the plane, a collection of two numbers is used.

CBSE Class 9 Maths Important Questions

Cbse study materials.

NCERT Solutions for Class 9 Maths Chapter 3 Coordinate Geometry

NCERT Solutions for Class 9 Maths Chapter 3 Coordinate Geometry are provided here. Our NCERT Maths solutions contain all the questions of the NCERT textbook that are solved and explained beautifully. Here you will get complete NCERT Solutions for Class 9 Maths Chapter 3 all exercises Exercise in one place. These solutions are prepared by the subject experts and as per the latest NCERT syllabus and guidelines. CBSE Class 9 Students who wish to score good marks in the maths exam must practice these questions regularly.

Class 9 Maths Chapter 3 Coordinate Geometry NCERT Solutions

Below we have provided the solutions of each exercise of the chapter. Go through the links to access the solutions of exercises you want. You should also check out our NCERT Class 9 Solutions for other subjects to score good marks in the exams.

NCERT Solutions for Class 9 Maths Chapter 3 Exercise 3.1

NCERT Solutions for Class 9 Maths Chapter 3 Exercise 3.2

NCERT Solutions for Class 9 Maths Chapter 3 Exercise 3.3

NCERT Solutions for Class 9 Maths Chapter 3 – Topic Discussion

Below we have listed the topics that have been discussed in this chapter.

• Cartesian System
• Plotting a Point in the Plane if its Coordinates are Given

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Unit 5: Coordinate Geometry

Coordinate plane.

• Introduction to the coordinate plane (Opens a modal)
• Points and quadrants example (Opens a modal)
• Identify coordinates Get 3 of 4 questions to level up!
• Identify points Get 5 of 7 questions to level up!
• Cartesian plane nomenclature Get 3 of 4 questions to level up!
• Quadrants on the coordinate plane Get 5 of 7 questions to level up!

Slope of a line

• Intro to slope (Opens a modal)
• Positive & negative slope (Opens a modal)
• Worked example: slope from graph (Opens a modal)
• Graphing a line given point and slope (Opens a modal)
• Calculating slope from tables (Opens a modal)
• Worked example: slope from two points (Opens a modal)
• Slope review (Opens a modal)
• Slope from graph Get 3 of 4 questions to level up!
• Graphing from slope Get 3 of 4 questions to level up!
• Slope in a table Get 3 of 4 questions to level up!
• Slope from two points Get 3 of 4 questions to level up!

Horizontal and vertical lines

• Slope of a horizontal line (Opens a modal)
• Horizontal & vertical lines (Opens a modal)
• Horizontal & vertical lines Get 5 of 7 questions to level up!

x-intercepts and y-intercepts

• Intro to intercepts (Opens a modal)
• x-intercept of a line (Opens a modal)
• Intercepts from an equation (Opens a modal)
• Intercepts from a table (Opens a modal)
• Intercepts of lines review (x-intercepts and y-intercepts) (Opens a modal)
• Intercepts from a graph Get 3 of 4 questions to level up!
• Intercepts from an equation Get 3 of 4 questions to level up!
• Intercepts from a table Get 3 of 4 questions to level up!

Applying intercepts and slope

• Slope, x-intercept, y-intercept meaning in context (Opens a modal)
• Slope and intercept meaning in context (Opens a modal)
• Slope and intercept meaning from a table (Opens a modal)
• Finding slope and intercepts from tables (Opens a modal)
• Linear functions word problem: fuel (Opens a modal)
• Using slope and intercepts in context Get 3 of 4 questions to level up!
• Linear equations word problems: tables Get 3 of 4 questions to level up!
• Linear equations word problems: graphs Get 3 of 4 questions to level up!
• Graphing linear relationships word problems Get 3 of 4 questions to level up!

Intro to slope-intercept form

• Intro to slope-intercept form (Opens a modal)
• Slope and y-intercept from equation (Opens a modal)
• Worked examples: slope-intercept intro (Opens a modal)
• Linear equation word problems (Opens a modal)
• Slope-intercept intro Get 3 of 4 questions to level up!
• Linear equations word problems Get 3 of 4 questions to level up!

Graphing slope-intercept equations

• Graph from slope-intercept equation (Opens a modal)
• Graphing slope-intercept form (Opens a modal)
• Graphing lines from slope-intercept form review (Opens a modal)
• Graph from slope-intercept form Get 3 of 4 questions to level up!

Point slope form

• Intro to point-slope form (Opens a modal)
• Point-slope & slope-intercept equations (Opens a modal)
• Point-slope form review (Opens a modal)
• Point-slope form Get 3 of 4 questions to level up!

Standard form

• Intro to linear equation standard form (Opens a modal)
• Graphing a linear equation: 5x+2y=20 (Opens a modal)
• Clarifying standard form rules (Opens a modal)
• Converting from slope-intercept to standard form (Opens a modal)
• Standard form review (Opens a modal)
• Graph from linear standard form Get 3 of 4 questions to level up!
• Convert linear equations to standard form Get 3 of 4 questions to level up!

• School Guide
• Class 10 Syllabus
• Maths Notes Class 10
• Science Notes Class 10
• History Notes Class 10
• Geography Notes Class 10
• Political Science Notes Class 10
• NCERT Soln. Class 10 Maths
• RD Sharma Soln. Class 10
• Math Formulas Class 10
• GRE Algebra | Coordinate Geometry | Set 2
• Coordinate Geometry
• Area of a Triangle in Coordinate Geometry
• Geometry Questions
• NCERT Solutions for Class 9 Maths Chapter 3 Coordinate Geometry
• NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry
• Class 8 NCERT Solutions - Chapter 4 Practical Geometry - Exercise 4.4
• Class 8 NCERT Solutions - Chapter 4 Practical Geometry - Exercise 4.5
• Class 8 NCERT Solutions - Chapter 4 Practical Geometry - Exercise 4.3
• Coordinate systems in ggplot2
• Class 8 NCERT Solutions - Chapter 4 Practical Geometry - Exercise 4.1
• Real-life Applications of Coordinate Geometry
• What are Coordinate Geometry Formulas?
• Class 9 NCERT Solutions - Chapter 3 Coordinate Geometry - Exercise 3.2
• Coordinate Axes in Coordinate Geometry
• Class 9 NCERT Solutions - Chapter 3 Coordinate Geometry - Exercise 3.3
• Class 10 NCERT Solutions- Chapter 7 Coordinate Geometry - Exercise 7.2
• Class 9 NCERT Solutions - Chapter 3 Coordinate Geometry - Exercise 3.1
• GRE Algebra | Coordinate Geometry

Practice Questions on Coordinate Geometry

In this article, we will learn about one interesting topic which is covered in class 9 and class 10 mathematics. We will look at some formulas and problems of Coordinate Geometry .

Important Formulas

General Form of a Line : Ax + By + C = 0 Slope Intercept Form of a Line : y = mx + c Point-Slope Form : y − y1= m(x − x1) The slope of a Line Using Coordinates : m = Δy/Δx = (y2 − y1)/(x2 − x1) The slope of a Line Using General Equation : m = −(A/B) Intercept-Intercept Form : x/a + y/b = 1 Distance Formula : |P1P2| = √[(x2 − x1) 2 + (y2 − y1) 2 ] For Parallel Lines : m1 = m2 For Perpendicular Lines : m1m2 = -1 Midpoint Formula : M (x, y) = [½(x1 + x2), ½(y1 + y2)] Angle Formula : tan θ = [(m1 – m2)/ (1 + m1m2)] Area of a Triangle Formula = ½ |x1(y2−y3)+x2(y3–y1)+x3(y1–y2)| Distance from a Point to a Line : d = [|Ax 0 + By 0 + C| / √(A 2 + B 2 )]

Practice Problems with Solutions:

Q1. find the equation of a line which passes through the points (3, 4) and (5, 8) in the general form..

To find the equation of a line in the general form, follow these steps: Step 1: Find the slope (m): m= (8-4)/(5-3) m = 2 Step 2: Use the point slope form through (3, 4) y – 4 = 2(x – 3) y – 4 = 2x – 6 y = 2x – 2 Step 3: Now, convert to the general form 2x – y – 2 =0

Q2. Find the equation of a line passing through the point (2, 3) with slope 2 in slope-intercept form y=mx+c.

The point-slope form equation of line is y – y1 = m(x – x1) Given point = (2, 3) slope = m =2 Now, y – 3 = 2(x – 2) y – 3 = 2x – 4 y = 2x – 1 So, the equation of a line passing through the point (2, 3) with slope 2 is y = 2x – 1.

Q3. Find the slope of the line passing through the points (2, 5) and (6, 9).

To find the slope of the line passing through the points (2, 5) and (6, 9), use the following formula m = (y2 – y1)/(x2 – x1) m = (9 – 5)/(6 – 2) m = 1. So, the slope of the line passing through the points (2, 5) and (6, 9) is 1.

Q4. Find the equation of a line with x-intercept 4 and y-intercept 5 in intercept-intercept form x/a+y/b=1.

Given, x-intercept = 4 y- intercept = 5 equation of line = x/a + y/b = 1. x/4 + y/5 = 1 5x + 4y = 20. So, the equation of a line with x-intercept and y-intercept is 5x + 4y = 20.

Q5. Find the distance between the points (2, 3) and (5, 7) using the distance formula.

The distance formula is d = √[(x2 − x1) 2 + (y2 − y1) 2 ] Given points are (2, 3) and (5, 7). Now, d = √[(5 – 2) 2 + (7 – 3) 2 d = √(3) 2 + (4) 2 d = √9 + 16 d = √25 d = 5 So, the distance between the points (2, 3) and (5, 7) is 5.

Q6. Determine if the lines with equations 2x+3y−5=0 and 4x+6y−10=0 are parallel.

To check whether the given pair of lines are parallel, we need to check their slope if m1 = m2, then they are parallel. Now, to calculate slope of first line 2x + 3y -5 = 0 m1 = -(a/b) m1 = -2/3 Now, we calculate slope of second line 4x + 6y – 10 = 0 m2 = -(a/b) m2 = -(4/6) m2 = -2/3 Here, m1 = m2 So, the lines 2x + 3y – 5 = 0 and 4x + 6y – 10 = 0 are parallel lines.

Q7. Determine if the lines with equations 3x+4y−7=0 and 4x−3y−5=0.

To check whether the given pair of lines are perpendicular, we need to check their slope if m1.m2 = -1, then they are perpendicular. Now, to calculate slope of first line 3x + 4y – 7 = 0 m1 = -(a/b) m1 = -3/4 Now, we calculate slope of second line 4x – 3y – 5 = 0 m2 = -(a/b) m2 = -(4/-3) m2 = 4/3 now, m1.m2 = (-3/4).(4/3) = -1 So, the lines 2x + 3y – 5 = 0 and 4x + 6y – 10 = 0 are perpendicular lines .

Q8. Find the midpoint of the line segment with endpoints (1, 2) and (5, 8).

to find the midpoint use the following formula M(x, y) = [(x1 + x2)/2, (y1 + y2)/2] now, M(x, y) = [(1+5)/2, (2+8)/2] M(x, y) = [6/2, 10/2] M(x, y) = (3, 5) Hence, the middle point is (3, 5).

Q9. Find the area of the triangle formed by the vertices (4, 5), (10, 12) and (-3, 2).

To find the area use the following formula Area = ½ |x1(y2−y3)+x2(y3–y1)+x3(y1–y2)| so, area of triangle = x1y2 – x1y3 + x2y3 – x2y1 + x3y1 – x3y2 area of triangle = 1/2 [4×12 – 4×2 + 10×2 – 10×(5) + (-3)×5 – (-3)×12] area of triangle = 1/2[48 – 8 + 20 – 50 – 15 + 36] area of triangle = 1/2[71] area of triangle = 71/2 So, the area of triangle is 71/2.

Q10. Find the distance from the point (2, 5) to the line 3x+4y−12=0.

To find the distance from a point to the line , use this formula d = [|Ax0 + By0 + C| / √(A 2 + B 2 )] Now, given line = (Ax + By + C = 0) = 3x + 4y -12 = 0 so, A = 3, B = 4 and C = -12 given point = (x0, y0) = (2, 5) So, x0 = 2, y0 = 5 d = [|Ax0 + By0 + C| / √(A2 + B2)] d = [|3 × 2 + 4 × 5 – 12| / √(3 2 + 4 2 )] d = [|6 + 20 – 12| / √(9 + 16)] d = [|14| / √(25)] d = 14/5 So, the distance from a point (2, 5) to the line (3x + 4y – 12 = 0) is 14/5

Unsolved questions

Q1. Find the equation of a line passing through the points (-1, 3) and (2, -5) in the general form Ax+By+C=0.

Q2. Find the equation of a line passing through the point (3, -2) with slope -1 in slope-intercept form y=mx+c.

Q3. Find the equation of the line passing through the point (-4, 6) with slope 4 in point-slope form 𝑦 − 𝑦1 = 𝑚(𝑥 − 𝑥1).

Q4. Find the slope of the line passing through the points (-3, 5) and (7, 2).

Q5. Find the slope of the line represented by the equation 2x−3y+6=0.

Q6. Find the equation of a line with x-intercept 3 and y-intercept -4 in intercept-intercept form x/a+y/b=1.

Q7. Determine if the lines with equations 4x+2y−8=0 and 8x+4y−16=0 are parallel.

Q8. Determine if the lines with equations 5x+2y−10=0 and 2x−5y+15=0 are perpendicular.

Q9. Find the distance between the points (-2, 4) and (6, -1) using the distance formula.

Q10. Find the midpoint of the line segment with endpoints (-3, 7) and (5, -4).

Related Articles:

FAQs on Coordinate Geometry

What are coordinate geometry.

Coordinate geometry is a system in which we makes use of the coordinate points to study the geometry. It is also used to describe the link between the geometry and the algebra.

Find the slope of the line 4x – 6y = 12

To find the slope of the line 4x – 6y = 12, slope = -(4/(-6)) slope = 2/3

What methods can be used to solve coordinate geometry?

To solve coordinate geometry, we can use formulas like stance formula, slope formula, midpoint formula, the equation of a line, etc .

What does it mean when two pair of lines are parallel?

When two pair of lines are parallel, that means their slopes are equal

What does it mean when two pair of lines are perpendicular?

When two pair of lines are perpendicular, that means the product of the slopes is = -1.

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Class 9 Maths Chapter 3 Coordinate Geometry MCQs

Class 9 Maths Chapter 3 Coordinate Geometry MCQs   are available here online. The objective questions are provided with their respective answers and detailed explanations. The Coordinate Geometry MCQs are prepared for Class 9 students as per the latest exam pattern. Students can practise these questions and score good marks in the final exam. These selective questions are given here, as per the CBSE syllabus (2022-2023) and NCERT guidelines. Also, check Important Questions for Class 9 Maths .

Download the below PDF to get more MCQs on Class 9 Maths Chapter 3 Coordinate Geometry.

Class 9 Maths Chapter 3 Coordinate Geometry MCQs – Download PDF

MCQs on Class 9 Maths  Chapter 3 Coordinate Geometry

Students can solve the multiple-choice problems given below to increase their problem-solving skills. Each question has 4 multiple options. Students need to choose the right answer.

1) The name of the horizontal line in the cartesian plane which determines the position of a point is called:

d. Quadrants

2) The name of the vertical line in the cartesian plane which determines the position of a point is called:

3) The section formed by horizontal and vertical lines determining the position of the point in a cartesian plane is called:

4) The point of intersection of horizontal and vertical lines determining the position of a point in a cartesian plane is called:

5) If the coordinates of a point are (0, -4), then it lies in:

c. At origin

d. Between x-axis and y-axis

Explanation: Since, x=0 and y=-4. Hence, the point will lie in the negative y-axis 4 units far from the origin.

6) If the coordinates of a point are (3, 0), then it lies in:

Explanation: Since, x = 3 and y = 0, therefore, the point will lie at the positive x-axis 3 units far from the origin.

7) If the coordinates of a point are (-3, 4), then it lies in:

a. First quadrant

b. Second quadrant

c. Third quadrant

d. Fourth quadrant

Explanation: Since x = -3 and y = 4, then if we plot the point in a plane, it lies in the second quadrant.

8) If the coordinates of a point are (-3, -4), then it lies in:

Explanation: Since, x = -3 and y = -4, then if we plot the point in a plane, it lies in the third quadrant.

9) Points (1, 2), (-2, -3), (2, -3);

b. Do not lie in the same quadrant

10) If x coordinate of a point is zero, then the point lies on:

11) Signs of the abscissa and ordinate of a point in the second quadrant are respectively 

b. +, –

d. -, –

Explanation: The signs of abscissa (x-value) and ordinate(y-value) in the second quadrant are – and + respectively.

12) The point (-10, 0) lies in

a. Third quadrant

b. Fourth quadrant

c. On the negative direction of the x-axis

d. On the negative direction of the y-axis

Explanation: The point (-10, 0) lies in the negative direction of the x-axis. 

13) A quadrant in which both x and y values are negative is

Explanation: In the third quadrant, both the abscissa and ordinate values are negative. Example (-2, -2), which lies in the third quadrant.

14) Abscissa of all the points on the x-axis is

d. Any number

Explanation: Abscissa of all the points on the x-axis can be any number. The coordinates of any point on the x-axis is (x, 0), where x can take any value.

15) Ordinate of all points on the x-axis is

Explanation: The ordinate of all points on the x-axis is 0. We know that the coordinates of any point on the x-axis is (x, 0). Here, the abscissa can take any value and the ordinate is zero.

16) Abscissa of a point is positive in

a. I quadrant

b. I and II quadrants

c. II quadrant only

d. I and IV quadrants

Explanation: In a coordinate plane, x can take positive values in the first and fourth quadrants. For example, (2, 2) and (2, -4) lie on the first and fourth quadrants, respectively.

17) Points (1, -1), (2, -2), (4, -5), (-3, -4) 

a. lie in II quadrant

b. lie in III quadrant

c. lie in IV quadrant

d. Does not lie in the same quadrant

Explanation: The point (1, -1), (2, -2) and (4, -5) lies in the fourth quadrant, where (-3, -4) lies in the third quadrant. 

18) Abscissa of all the points on the y-axis is

Explanation: The abscissa of all the points on the y-axis is 0. We know that the coordinates of any point on the y-axis is (0, y). Here, the ordinate can take any value and the abscissa is zero.

19) Ordinate of all the points on the y-axis is

Explanation: The ordinate of all the points on the y-axis can be any number. The coordinates of any point on the y-axis is (0, y). Here, abscissa can take only the value of 0 and the ordinate can take any value.

20) The point which lies on the y-axis at a distance of 5 units in the negative direction of the y-axis is

Explanation: The coordinates of any point on the y-axis is (0, y).

Hence, abscissa should be 0. 

Given that, the point lies in the negative direction of the y-axis. Hence, the value of y should be negative. 

Therefore, the point which lies on the y-axis at a distance of 5 units in the negative direction is (0, -5).

Class 9 Related Articles on Coordinate Geometry

• Coordinate Geometry Class 9 Notes – Chapter 3
• Coordinate Geometry Formulas
• Important Questions Class 9 Maths Chapter 3-Coordinate Geometry
• Two Dimensional Coordinate Geometry

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