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1. 1. Find the coordinates of the point equidistant
from the points A(1, 2), B (3, –4) and C(5, –6).
(a) (2, 3)
(b) (–1, –2)
(c) (0, 3)
(d) (1, 3)
2. Find the coordinates of the point equidistant
from the points A(5, 1), B(–3, –7) and C(7, –1).
(a) (2, –4)
(b) (3, –6)
(c) (4, 7)
(d) (8, –6)
3. Two of the vertices of a triangle ABC are given
by A(6, 4) and B(–2, 2) and its centroid is G(3, 4).
Find the coordinates of the third vertex C of the
ΔABC.
(a) (2, 3)
(b) (4, 6)
(c) (4, 3)
(d) (5, 6)
4. Find the value of P for which the point (–1, 3),
(2, p) and (5, –1) are collinear.
(a) 4 (b) 3 (c) 2 (d) 1
5. Find the distance of the point (–6, 8) from the
origin.
(a) 8 (b) 11 (c) 10 (d) 9
6. Find the value of p for which the points (–5, 1),
(1, p) and (4, –2) are collinear.
(a) –3 (b) –2 (c) 0 (d) –1
7. Find the value of k if the points A(2, 3), B(4, k)
and C(6, –3) are collinear.
(a) 2 (b) 3 (c) 0 (d) 1
8. In what ratio of line x – y – 2 = 0 divides the line
segment joining (3, –1) and (8, 9)?
(a) 1 : 2 (b) 2 : 1 (c) 2 : 3 (d) 1 : 3
9. Find the ratio in which the line joining the
points (6, 4) and (1, –7) is divided by x-axis.
(a) 1 : 3
(b) 2 : 7
(c) 4 : 7
(d) 6 : 7
10. The point on x-axis which is equidistant
from the points A(-1, 0) and B(5,0) is
(a) (0,2)
(b) (2,0)
(c) (3,0)
(d) (0,3)
11. The distance of the point P(-6,8) from the
origin is
(a) 8
(b) 2√7
(c) 6
(d) 10
12. If R(5,6) is the midpoint of the line segment
AB joining the points A(6,5) and B(4,4)
then y equals
(a) 5
(b) 7
(c) 12
(d) 6
13. If the point C(k,4) divides the join of the
points A(2,6) and B(5,1) in the ratio 2:3
then the value of k is
(a) 16
(b) 28/5
(c) 16/5
(d) 8/5
14. The distance of the point (-3, 4) from x-axis
is
(a) 3
(b) -3
(c) 4
(d) 5
Answer(c)
15. The perimeter of the triangle with vertices
(0,4), (0,0) and (3,0) is
(a) 7 + √5
(b) 5
(c) 10
(d) 12
16. If A(1,3) B(-1,2) C(2,5) and D(x,4) are the
vertices of a ||gm ABCD then the value of x
is
(a) 3
(b) 4
(c) 0
(d) 3/2
17. The midpoint of segment AB is P(0,4). If
the coordinates of B are (-2, 3), then the
coordinates of A are
(a) (2,5)
(b) (-2,-5)
(c) (2,9)
(d) (-2,11)
18. If the points A(x,2), B(-3, -4) and C(7, -5)
are collinear then the value of x is
(a) -63 (b) 63 (c) 60 (d) -60
19. The area of a triangle with vertices A(5,0),
B(8,0) and C(8,4) in square units is
(a) 20
(b) 12
(c) 6
(d) 16
20. The coordinates of the point P dividing the
line segment joining the points A(1,3), and

2. B(4,6) in the ratio 2:1 is
(a) (2,4) (b) (3,5) (c) (4,2) (d) (5,3)
21. If the coordinates of one end of a diameter
of a circle are (2,3) and the coordinates of
its centre are (-2,5), then the coordinates of
the other end of the diameter are
(a) (-6,7)
(b) (6.-7)
(c) (4,2)
(d) (5,3)
22. If A(-6,7) and B(-1,-5) are two given points
then the distance 2AB is
(a) 13 (b) 26 (c) 169 (d) 238
23. ABCD is a rectangle whose three vertices
are B(4,0), C(4,3) and D(0,3) The length of
one of its diagonals is
(a) 5 (b) 4 (c) 3 (d) 245
24. Which point on x-axis is equidistant from
the points A(7,6) and B(-3,4)
(a) (0,4) (b) (-4,0) (c) (3,0) (d) (0,3)
25. The distance of the point P(2, 3) from the x-
axis is
(a) 2 (b) 3 (c) 1 (d) 5
26. The distance between the point P(1, 4) and
Q(4, 0) is
(a) 4 (b) 5 (c) 6 (d) 3√3
27. The points (-5, 1), (1, p) and (4, -2) are
collinear if
the value of p is
(a) 3
(b) 2
(c) 1
(d) -1
28. The area of the triangle ABC with the vertices
A(-5, 7), B(-4, -5) and C(4, 5) is
(a) 63 (b) 35 (c) 53 (d) 36
29. The distance of the point (α, β) from the
origin is
(a) α + β
(b) α² + β²
(c) |α| + |β|
(d)
30. The area of the triangle whose vertices are
A(1, 2), B(-2, 3) and C(-3, -4) is
(a) 11 (b) 22 (c) 33 (d) 21
31. If the distance between the points (x, -1) and
(3, 2) is 5, then the value of x is
(a) -7 or -1
(b) -7 or 1
(c) 7 or 1
(d) 7 or -1
32. The area of the triangle formed by the points
A(-1.5, 3), B(6, -2) and C(-3, 4) is
(a) 0 (b) 1 (c) 2 (d) 3/2
33. If the points P(1, 2), B(0, 0) and C(a, b) are
collinear, then
(a) 2a = b
(b) a = -b
(c) a = 2b
(d) a = b
34. If the segment joining the points (a, b) and (c,
d) subtends a right angle at the origin, then
(a) ac - bd = 0
(b) ac + bd = 0
(c) ab + cd = 0
(d) ab - cd= 0
35. The mid-point of the line segment joining the
points A (-2, 8) and B (-6, -4) is
(a) (-4, -6)
(b) (2, 6)
(c) (-4, 2)
(d) (4, 2)
36. The distance of the point P(- 6, 8) from the
origin is
(a) 8 (b) 2√7 (c)
10 (d) 6
37. The distance of the point P(- 6, 8) from the
origin is
(a) 8 (b) 2√7 (c)
10 (d) 6
38. The distance between the points (0, 5) and (- 5,
0) is
(a) 5 (b) 5√2
(c)2√5 (d) 10
The perimeter of a triangle with vertices (0, 4), (0, 0)
and (3, 0) is
(a) 5 (b) 12 (c)11
(d)7+√5
39. The area of a triangle with vertices A(3,0), B(7,
0) and C(8, 4) is
(a) 14 (b) 28 (c) 8 (d) 6
40. The points (- 4, 0), (4, 0) and (0, 3) are the
vertices of a
(a) right angled triangle (b)
isosceles triangle
(c) equilateral triangle (d) scalene
triangle