CBSE Class 10 Maths Chapter 7 Coordinate Geometry Important Questions with Answers

CBSE Class 10 Maths Chapter 7 Coordinate Geometry Important Questions with Solutions 2022-23 : CBSE Board is set to conduct the annual CBSE class 10 board examination 2023. The board has already published the CBSE Sample papers with Marking Scheme for the current academic year for all subjects Wise.

We are going to discuss the CBSE important questions from Chapter 7 Coordinate Geometry of CBSE Class 10 Maths.  It carries a total number of weightage of 06 marks covering topics such as Concepts of coordinate geometry, graphs of linear equations. Distance formula. Section formula. Check Now More Important Questions With Solutions (MCQs, Short Types, Objective Types, Long Types Question with Solutions)

MULTIPLE CHOICE QUESTIONS

Ques-1. The distance of the point P (-6, 8) from the origin is:

(a) 14

(b) 6

(c) 8

(d) 10

Ans: (d) 10

Ques-2. If (a, b) is the mid-point of the line segment joining the points A (10, -6) and B (k, 4) and a – 2b = 18, the value of k is:

(a) 40

(b) 22

(c) 4

(d) 36

Ans: (b) 22

Ques-3. If the point P (k, 0) divides the line segment joining the points A (2, -2) and B (-7, 4) in the ratio 1:2, then the value of k is :

(a) 1

(b) 2

c) -1

(d) -2

Ans: c) -1

Ques-4. If the point P (6, 2) divides the line segment joining A (6, 5) and B (4, y) in the ratio 3 : 1, then the value of y is :

a) 4

(b) 2

(c) 1

(d) 3

Ans: (c) 1

Ques-5. Distance between two points (3, 2) and (6, 6) is:

(a) 5

(b) 3

(c) 2

(d) 8

Ans:(a) 5

Ques-6. The line segment joining the points P (-3, 2) and Q (5, 7) is divided by the y- axis in the ratio:

(a) 3 : 1

(b) 3 : 2

(c) 3 : 4

(d) 3 : 5

Ans: (d) 3 : 5

Ques-7. The point P on x- axis is equidistant from the points A (-1, 0) and B (5, 0) is:

(a) (2, 2)

(b) (0, 2)

(c) (2, 0)

(d) (3, 2)

Ans: (c) (2, 0)

SHORT ANSWER TYPE QUESTION ( 2 MARKS)

Ques-1. Find the point on the x-axis which is equidistant from the points (2, -5) and (-2, 9)

Ans: (-7,0)

Ques-2. Find the distance of the point P (2, 3) from the x-axis.

Ans:(3)

Ques-3. Find the ratio in which the point (-3, k) divides the line-segment joining the points (-5, 4) and (-2, 3). Also find the value of k.

Ans:

Ques-4. If A (5,2), B (2, -2) and C (-2, t) are the vertices of a right-angled triangle with ∠B = 90°, then find the value of t.

Ans: t=1

Ques-5. In what ratio does the point P (2, -5) divide the line segment joining A (-3, 5) and B (4, -9).

Ans :

SHORT ANSWER TYPE QUESTION ( 3 MARKS)

Ques-1. Determine if the points (1, 5), (2, 3) and (-2, -11) are collinear.

Ans:  Non – collinear

Ques-2. Find the values of y for which the distance between the points P (2, -3) and Q (10, y) is 10 units.

Ans : y=3 or y=-9

Ques-3. Find the area of a rhombus if its vertices are (3, 0), (4, 5), (-1, 4) and (-2, -1) taken in order.

Ans : 24 Square units

Ques-4. If A (-2,1), B (a, 0), C (4, b) and D (1, 2) are the vertices of a parallelogram ABCD, find the values of a and b. Hence find the lengths of its sides.

Ans :

Ques-5. If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order find x and y.

Ans : x=6 and y=3

LONG ANSWER TYPE QUESTIONS (4 MARKS)

Ques-1. The vertices of quadrilateral ABCD are A (5, -1), B (8,3), C (4, 0) and D (1, -4). Prove that ABCD is a rhombus.

Ans:

Ques-2. Find the centre and radius of the circumcircle (i.e., circumcentre and circum-radius) of the triangle whose vertices are (-2, 3), (2, -1) and (4, 0).

Ans:

Ques-3. Find the coordinates of the points of trisection (i.e., Points dividing in three equal parts) of the line segment joining the points A (2, -2) and B (-7, 4).

Ans= The Coordinates of the points of trisection of the line segment joining A and B are(-1, 0) and (-4, 2)

Ques-4. An equilateral triangle has one vertex at (3, 4) and another at (-2, 3). Find the co- ordinates of the third vertex.

Ans:

Ques-5. The three vertices of a parallelogram ABCD are A (3, -4), B (-1, -3) and C (-6, 2). Find the coordinates of vertex D and find the area of ABCD.

Ans: 15 Square Units

Ques-6. The base QR of an equilateral triangle PQR lies on x-axis. The co-ordinates of point Q are (-4, 0) and the origin is the mid-point of the base. Find the co-ordinates of the point P and R.

Ans: Coordinates of p are (0, 4√3) or (0, -√(3)