CBSE Class 10 Maths 2024-25: Chapter 7 Coordinate Geometry Important Competency-Based Questions with Answers; Download Free PDF

As the CBSE Class 10 board exams get closer, it’s important for students to understand the new exam pattern. Starting in the 2024-25 school year, CBSE will include 50% more competency-based questions. These questions will be both multiple choice and written, focusing on how to use what students have learned in real-life situations.

This article explores Chapter 7 Coordinate Geometry. It highlights key competency-based questions and provides answers to help students succeed.

Understanding Competency-Based Questions in Chapter 7 Coordinate Geometry

Competency-based questions are designed to see how well students can apply their knowledge in everyday life. They can come in different forms, such as case studies, true-false questions, gap-filling tasks, and long or short answer questions.

Competency-based questions in Chapter 7: Coordinate Geometry go beyond memorization, encouraging critical thinking and problem-solving. These questions help students grasp concepts deeply by applying them to real-world scenarios.

CBSE Class 10 Maths Chapter 7: Coordinate Geometry Important Competency-Based Questions

Multiple Choice Questions

Q.1 What is the distance between the points (-1, 3) and (2, -5)?

1. √5
2. √55
3. √65
4. √73

Answer. (4)

Q.2 A circle of radius 5 units has its centre at (-2, 2). The point (-6, y ) lies on the circle. Which of these could be the value of y ?

1. -3
2. 1
3. 5
4. 6

Answer. (3)

Q.3 P(1, 7), Q(-3, 2) and R(6, 1) are the coordinates of the vertices of a triangle. Which of the following types of triangle is ΔPQR?

1. Scalene triangle
2. Equilateral triangle
3. Isosceles right-angled triangle
4. Isosceles acute-angled triangle

Answer. (1)

Q.4 In the SQUARE given below, the coordinates of two adjacent vertices P and Q are given.

What are the coordinates of vertex R?

1. (-4, -2)
2. (8, 2)
3. (8, -2)
4. (-4, 2)

Answer. (3)

Q.5 ΔPQR is a triangle such that PQ:PR = 1:2. Point P lies on the x -axis and the coordinates of Q and R are known.

Which of the following formula can DEFINITELY be used to find the coordinates of P?

i) Section formula
ii) Distance formula

1. only i)
2. only ii)
3. both i) and ii)
4. neither i) or ii)

Answer. (2)

Q.6 Which one of these is the relation between x and y if ( x, y ) is equidistant from (-1, 4) and (2, 5)?

1. 3 x - y = 6
2. 6 x + 2 y = - 9
3. 3 x + y = 6
4. 3 x - y = 3

Answer. (3)

Q.7 What is the distance of (7, -3) from the origin?

1. 7 units
2. √40 units
3. √21 units
4. √58 units

Answer. (4)

Q.8 Which of the following points is the mid-point of the line segment joining P(5, 2) and Q(7, 6)?

1. (1, 2)
2. (6, 4)
3. (2, 4)
4. (4, 4)

Answer. (2)

Free Response Questions

Q.9 The point ( x, y ) is equidistant from (-4, 0) and (5, 3).

Write an equation relating x and y. Show your steps.

Answer. Applies the distance formula correctly to write √{( x + 4)² + y ² } = √{( x - 5) ² + ( y - 3) ² }

Writes the relation as 3 x + y = 3.

Q.10 In what ratio does the origin divides line segment joining A(-5, 0) and B(3, 0)? Show your work.

Answer. Writes the distance of A from the origin is 5 units and that of B from the origin is 3 units.

Hence, the ratio in which the origin divides the line segment AB is 5:3

(Award full marks if student uses any other method using calculation.)

Q.11 A(6, 8), B(3, 7) and C(4, 4) are the vertices of a right-angled triangle, where ∠B = 90°. Find the area of the triangle. Show your work

Answer. Identifies height of triangle = AB and base of triangle = BC. 

Finds height = AB = √ {(-3)² + (-1)² } = √10 units and base = BC = √{(1² + (-3)² )} = √10 units.

Q.12 F lies on the line segment joining E(-3, 2) and G(4, 5). F divides EG in the ratio 2:1. Find the coordinates of F. Show your work.

Answer. Uses the section formula to find the coordinates of the point F as follows:

Q.13 In the figure given below, AB is the diameter of the circle with centre O and OB is the diameter of the circle with centre C.

Find the coordinates of point C. Show your steps.

Answer. Finds the coordinates of B using the mid-point formula as B(5, 10). Working may look like:

Let co-ordinates of B be ( x, y )

Q.14 Shown below is a right triangle ABC.

Find the value of cos C. Show your work.

Answer. Finds the coordinates of B as (2, -1). 

Uses the distance formula and finds AC = √(5² + 4² ) = √41 units and BC = √(5) ² = 5 units.

Q.15 Find the ratio in which O(4, 3) divides the line segment joining A(2, 1) and B(7, 6). Show your work.

Answer. Finds the distances using the distance formula:

1 AO = √8 = 2√2 units
BO = √18 = 3√2 units

Hence, the ratio in which O(4, 3) divides the line segment AB is 2:3.

(Award full marks if the student correctly solves the same using the Section Formula.)

Q.16 Find the length of the longest side of the triangle formed by the points of intersection of line 8 x + 6 y = 48 with the coordinate axes. Show your work.

Answer. Substitutes x and y as 0 in the given equation 8 x + 6 y = 48 to find the coordinates of the points of intersection as (0, 8) and (6, 0) respectively.

Uses the distance formula to find the length of the longest side of the triangle as √{(0 - 6)² + (8 - 0)² } = 10 units.

Q17. A square is inscribed in a circle of radius 2 cm with center O at the origin. All 4 vertices of the square lie on the coordinate axes. Use the distance formula to find the length of the side of the square. Show your work

Answer. Writes that the coordinates of the vertices of the circle would be (2, 0), (0, -2), (-2, 0), (0, 2).

Uses the distance formula and any 2 adjacent coordinates of the vertices of the square to find the length of the side of the square as 2√2 cm.

Case Study

Answer the questions based on the given information.

Nidhi and Shikha have planned to meet at a park. Nidhi's house is at point A, and the park is at point B as shown in the below figure. Shikha's house is at point C, the coordinates of which are unknown.

Points A, B, and C lie on a straight line. The park divides the line connecting their houses such that AB:BC = 3:2.

Q.18 Find the coordinates of Shikha's house.

Answer. Uses the section formula by considering C( m,n ) and dividing line AC such that AB:BC = 3:2 to write:

Solves the above system of equations to obtain 3 m = 9 and 3 n = 24 to find m = 3 and n = 8.

Hence obtains the coordinates of Shikha's house as C(3, 8).

Q.19 Find the distance between Nidhi's house and the Park.

Answer. Uses the distance formula to find the distance between Nidhi's house and the park as:

√(1 - (-2)) ² + (6 - 3) ² = √18 = 3√2 units

Q.20 Find the distance between Nidhi's house and Shikha's house.

Answer. Writes coordinates of Nidhi's house as A(-2, 3) and Shikha's house as C(3, 8).

Uses the distance formula to find the distance between their houses as √(3 - (-2)) ² +(8 - 3) ² = √50 units = 5√2 units.

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