CBSE Class 10 Mathematics Coordinate Geometry Worksheet Set 03

Choose the correct answer from the given options:

Question. The point which lies on the perpendicular bisector of the line segment joining the points A(– 2, – 5) and B(2, 5) is
(a) (0, 0)
(b) (0, 2)
(c) (2, 0)
(d) (– 2, 0)
Answer : A

Question. The point which divides the line segment joining the points A(0, 5) and B(5, 0) internally in the ratio 2 : 3 is
(a) (2, 3)
(b) (3, 4)
(c) (–2, 3)
(d) (3, –5)
Answer : A

Question. The ratio in which the y-axis divides the line segment joining the points (5, –6) and (–1, –4) is
(a) 1 : 5
(b) 5 : 1
(c) 1 : 7
(d) 7 : 1
Answer : B

Question.  If A(1, 2), B(4, 3) and C(6, 6) are three vertices of parallelogram ABCD, coordinates of D are
(a) (3, 5)
(b) (2, 7)
(c) (4, 9)
(d) (3, 8)
Answer : A

Question. P(–2, 5) and Q(3, 2) are two points. The coordinates of the point R on PQ such that PR = 2QR are
(a) R(4/3, 3)
(b) R(2/3, 5)
(c) R(1/3, 7)
(d) None of these
Answer : A

Question. The coordinates of a point A, where AB is a diameter of the circle with centre (–2, 2) and B is the point with coordinates (3, 4) are
(a) A(7, 0)
(b) A(5, 0)
(c) A(–5, 0)
(d) A(–7, 0)
Answer : D

Question. The mid-point of the line segment joining the points (–5, 7) and (–1, 3) is
(a) (–3, 7)
(b) (–3, 5)
(c) (–1, 5)
(d) (5, –3)
Answer : B

Question.  The value of a, for which point P (a/3, 2) is the mid-point of the line segment joining the points Q(–5, 4) and R(–1, 0) is
(a) –5
(b) –7
(c) –9
(d) –11
Answer : C

Question. The coordinates of the point which divides the line segment joining the points (4, –3) and (8, 5) in the ratio 3 : 1 internally are
(a) P(4, 3)
(b) P(7, 3)
(c) P(3, 5)
(d) P(7, 3)
Answer : D

Question. If the point P(m, 3) lies on the line segment joining the points A − (2/5, 6) and B(2, 8), the value of m is
(a) 3
(b) 2
(c) –3
(d) –4
Answer : D

Question. If (3, –6) is the mid-point of the line segment joining (0, 0) and (x, y), then the point (x, y) is
(a) (–3, 6)
(b) (6, –6)
(c) (6, –12)
(d) (3/2, 3)
Answer : C

Question. If the point C(–1, 2) divides internally the line segment joining A(2, 5) and B in ratio 3 : 4, the coordinates of B are
(a) B(5, 2)
(b) B(–5, –2)
(c) B(–7, 2)
(d) B(7, –2)
Answer : B

Question. The ratio in which the line segment joining the points (6, 4) and (1, –7) is divided by x-axis is
(a) 4 : 7
(b) 4 : 5
(c) 4 : 9
(d) 4 : 11
Answer : A

Question. The coordinates of the point P which divides the join of A(–2, 5) and B(3, –5) in the ratio 2 : 3 are
(a) (1, 0)
(b) (2, 0)
(c) (3, 0)
(d) (0, 1)
Answer : D

Question. The centre of a circle is (2a, a – 7). The value of a if the circle passes through the point (11, –9) and has diameter 10√2 units is
(a) a = 3 or 6
(b) a = 5 or 3
(c) a = 7 or 4
(d) None of these
Answer : B

Question. The value(s) of x for which the distance between the points P(x, 4) and Q(9, 10) is 10 units, is
(a) 15 or 2
(b) 10 or 9
(c) 17 or 1
(d) None of these
Answer : C
 

Assertion-Reason Type Questions

In the following questions, a statement of assertion (A) is followed by a statement reason (R). Choose the correct choice as:
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.

Question. Assertion (A): The point (–1, 6) divides the line segment joining the points (–3, 10) and (6, –8) in the ratio 2 : 7 internally.
Reason (R): Given three points, i.e. A, B, C form an equilateral triangle, then AB = BC = AC.
Answer : B

Question. Assertion (A): Mid-point of a line segment divides line in the ratio 1 : 1.
Reason (R): The ratio in which the point (–3, k) divides the line segment joining the points (–5, 4) and (–2, 3) is 1 : 2.
Answer : C
 

Very Short Answer type Questions

Question. If the point A(0, 2) is equidistant from the points B( 3, p) and C(p, 5), find the value of p. Also, find the length of AB.
Answer : p = 1, AB = 10 units

Question. Find the ratio in which the line segment joining the points (– 3, 10) and (6, – 8) is divided by (– 1, 6).
Answer : 2 : 7

Question. Find the relation between x and y such that the point P(x, y) is equidistant from the points A(1, 4) and B(−1, 2).
Answer : y = 3 − x

Question. Find the point on the x-axis which is equidistant from (2, –5) and (–2, 9).
Answer : (– 7, 0)

Question. Find the ratio in which the line segment joining A(1, – 5) and B(– 4, 5) is divided by the x-axis. Also find the coordinates of the point of division.
Answer : 1 : 1 ; (- 2/3, 0)

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

Question. Check whether (5, – 2), (6, 4) and (7, – 2) are the vertices of an isosceles triangle.
Answer : Yes
 

Short Answer type Questions

Please click on below link to download CBSE Class 10 Mathematics Coordinate Geometry Worksheet Set C