CBSE Class 10 Mathematics Coordinate Geometry Worksheet Set H

Question. The point on the x-axis which is equidistant from (– 4, 0) and (10, 0) is:
(a) (7, 0)
(b) (5, 0)
(c) (0, 0)
(d) (3, 0)
Answer : D

Question. The centre of a circle whose end points of a diameter are (– 6, 3) and (6, 4) are:
(a) (8, – 1)
(b) (4, 7)
(c) (0, 2/7)
(d) (4, 2/7)
Answer : C

Question. The distance between the points (m, – n) and (– m, n) is:
(a) √m² +n²
(b) m + n
(c) 2 √m² + n²
(d) √2m² + 2n²
Answer : C

Question. The point which divides the line segment joining the points (7, –6) and (3, 4) in the ratio 1:2 internally, lies in the:
(a) I quadrant
(b) II quadrant
(c) III quadrant
(d) IV quadrant
Answer : D

Question. The distance between the points (a cos θ + b sin θ, 0) and (0, a sin θ – b cos θ), is
(a) a² + b²
(b) a2 – b²
(c) √a² + b²
(d) √a² – b²
Answer : C

Question. The point which lies on the perpendicular bisector of the line segment joining point A (–2, –5) and B (2, 5) is:
(a) (0, 0)
(b) (0, –1)
(c) (–1, 0)
(d) (1, 0)
Answer : A

Question. The fourth vertex D of a parallelogram ABCD whose three vertices are A (–2, 3), B (6, 7) and C (8, 3) is:
(a) (0, 1)
(b) (0, –1)
(c) (–1, 0)
(d) (1, 0)
Answer : B

Question. 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) –2
(d) –1
Answer : D

Question. The distance of the point p(-3, -4) from the x-axis (in units) is:
(a) 3
(b) –3
(c) 4
(d) 5
Answer : C

Question. If the point P(2, 1) lies on the line segment joining points A(4, 2) and B(8, 4), then:
(a) AP = 1/3 AB 
(b) AP = PB
(c) PB = 1/3 AB 
(d) AP = 1/2 AB
Answer : D

Question. If A , (m/3, 5) is the mid-point of the line segment joining the points Q(–6, 7) and R(–2, 3), then the value of m is:
(a) -12
(b) -4
(c) 12
(d) -6
Answer : A

Question. The perimeter of a triangle ABC with vertices A (0, 4), B (0, 0) and C (3, 0) is:
(a) 5 units
(b) 11 units
(c) 12 units
(d) (7 + 5) units
Answer : C

Question. If P (a/3, 4) is the midpoint of the line segment joining the points Q(–6, 5) and R(–2, 3), then the value of a is:
(a) –4
(b) –12
(c) 12
(d) –6
Answer : B

Question. The perpendicular bisector of the line segment joining the points A(1, 5) and B(4, 6) cuts the y-axis at:
(a) (0, 13)
(b) (0, –13)
(c) (0, 12)
(d) (13, 0)
Answer : A

Question. The coordinates of the point which is equidistant from the three vertices of the ΔAOB as shown in the figure is: 

(a) (x, y)
(b) (y, x)
(c) (x/2, y/2)
(d) (y/2, x/2)
Answer : A

Question. A circle drawn with origin as the centre passes through (13/2, 0) The point which does not lie in the interior of the circle is:
(a) (-3/4, 1)
(b) (2, 7/3)
(c) (5, 1/2)
(d) (-6, 5/2)
Answer : D

Fill in the Blanks

Fill in the blanks/tables with suitable information:

Question. AOBC is a rectangle whose three vertices are A(0, –3), O(0, 0) and B(4, 0). The length of its diagonal is .............................. . 
Answer : 5

Question. The centroid of the triangle whose vertices are (4, – 8), (– 9, 7) and (8, 13) is .............................. .
Answer : (1, 4)

Question. The ratio in which x-axis divides the line segment joining the point (2, 3) and (4, – 8) is .............................. .
Answer : 3.8

Question. The mid-point of the line segment AB is (4, 0).
If the co-ordinates of point A is (3,–2), then coordinates of point B is .............................. .
Answer : B (3, 2)

Question. Distance of a point (–24, 7) from the origin (in units) is .............................. .
Answer : 25 units

Question. If P(–1, 1) is the mid-point of the line segment joining the points A(–3, b) and B(1, b + 4) then b = ...............................
Answer : –1

Write True or False

Question. ΔABC with vertices A(–2, 0), B(2, 0) and C(0, 2) is similar to DDEF with vertices D(–4, 0), E(4, 0) and F(0, 4). 
Answer : True.

Question. Point P (–4, 2) lies on the line segment joining the points A (–4, 6) and B (–4, –6).
Answer : True.

Question. Points A(4, 3), B(6, 4), C(5, –6) and D(–3, 5) are the vertices of a parallelogram.
Answer : False.

Question. Point P(5, –3) is one of the two points of trisection of the line segment joining points A(7, –2) and B(1, –5).
Answer : True.

Question. Point P(–2, 4) lies on a circle of radius 6 and centre C(3, 5). [CBSE 2014, 13]
Answer : False.

Question. The points A (–1, –2), B (4, 3), C (2, 5) and D (–3, 0) in that order from a rectangle.
Answer : True.

Question. Find the area of the triangle formed by the points O (0,0), A(a,0) and B(0,h).
Answer : ab/2

Question. Find the area of ∆ABC where A (2,3), B (-2,1) and C (3,-2)
Answer : 11sq. units

Question. Find the distance between the prints A(10 Cosθ) and B(0,10 Sinθ)
Answer : 10

Question. Find the distance of the point (3,-4) from y-axis If A(3,2) , B(-2,1) are two vertices of ∆ABC whose centroid G has the co-ordinates (5/3, 1/3). Find the co-ordinates of the third vertex C.
Answer : 3 units

Question. AB is the diameter of a circle whose centre is (2,-3). If the co-ordinates of A.B are (1,4), then find the co-ordinates of A.
Answer : (3,-10)

Question. Find the ratio in which the line-segment joining the points (-3,-4) and (1,-2) is divided by y-axis
Answer : 3:1

Question. If the area of a triangle formed by (x, 2x), (-2, 6) and (3,1) is 5 square units, then find the value of x.
Answer : x = 2

Question. Find the co-ordinates of the point which divides the line-segment joining the point (1,3) and (2,7) in the ratio 3:4
Answer : 10/7, 33/7

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