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.1. The distance of the point P(2, 3) from the x-axis is
(a) 2
(b) 3
(c) 1
(d) 5
2. The distance between the point P(1, 4) and Q(4, 0) is
(a) 4
(b) 5
(c) 6
(d) 3√3
3. 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
4. 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
5. The distance of the point (α, β) from the origin is
(a) α + β
(b) α² + β²
(c) |α| + |β|
(d) root of α2+β2
6. 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
7. The line segment joining the points (3, -1) and (-6, 5) is trisected. The coordinates of point of trisection are
(a) (3, 3)
(b) (- 3, 3)
(c) (3, – 3)
(d) (-3,-3)
8. The line 3x + y – 9 = 0 divides the line joining the points (1, 3) and (2, 7) internally in the ratio
(a) 3 : 4
(b) 3 : 2
(c) 2 : 3
(d) 4 : 3
9. The distance between A (a + b, a – b) and B(a – b, -a – b) is
10. If (a/3, 4) is the mid-point of the segment joining the points P(-6, 5) and R(-2, 3), then the value of ‘a’ is
(a) 12
(b) -6
(c) -12
(d) -4
11. 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
12. The points (1,1), (-2, 7) and (3, -3) are
(a) vertices of an equilateral triangle
(b) collinear
(c) vertices of an isosceles triangle
(d) none of these
13. The coordinates of the centroid of a triangle whose vertices are (0, 6), (8,12) and (8, 0) is
(a) (4, 6)
(b) (16, 6)
(c) (8, 6)
(d) (16/3, 6)
14. Two vertices of a triangle are (3, – 5) and (- 7,4). If its centroid is (2, -1), then the third vertex is
(a) (10, 2)
(b) (-10,2)
(c) (10,-2)
(d) (-10,-2)
15. 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
16. 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
17. If the distance between the points (2, –2) and (–1, x) is 5, one of the values of x is
(A) –2
(B) 2
(C) –1
(D) 1
18.. 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)
19. The points A (9, 0), B (9, 6), C (–9, 6) and D (–9, 0) are the vertices of a
(A) Square
(B) Rectangle
(C) Rhombus
(D) Trapezium
20.. The distance of the point P (2, 3) from the x-axis is
(A) 2
(B) 3
(C) 1
(D) 5
21. The distance between the points A (0, 6) and B (0, –2) is
(A) 6
(B) 8
.22. AOBC is a rectangle whose three vertices are vertices A (0, 3), O (0, 0) and B (5, 0). The length of its diagonal is
(A) 5
(B) 3
(C) √34
(D) 4
23.. If P (a/3, 4) is the mid-point 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
.24 The coordinates of the point which is equidistant from the three vertices of the Δ AOB as shown in the figure is:
(A) (x, y)
(B) (y, x)
(C) (x/2, y/2)
(D) (y/2, x/2)
25. A circle drawn with origin as the centre passes through The point which does not lie in the interior of the circle is
(C) (5, –1/2)
(D) (–6, 5/2)
26. If the distance between the points (4, p) and (1, 0) is 5, then the value of p is
(A) 4 only
(B) ± 4
(C) – 4 only
(D) 0
27. 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
28. The point which divides the line segment joining the points (7, –6) and (3, 4) in ratio 1 : 2 internally lies in the
(A) I quadrant
(B) II quadrant
(C) III quadrant
(D) IV quadrant
29 One of the two points of trisection of the line segment joining the points A (7, – 2) and B (1, – 5) which divides the line in the ratio 1:2 are:
(A) (5, –3)
(B) (5, 3)
(C) (–5, –3)
(D) (13, 0)
30. A line intersects the y-axis and x-axis at the points P and Q, respectively. If (2, –5) is the mid - point of PQ, then the coordinates of P and Q are, respectively.
(A) (0, – 5) and (2, 0)
(B) (0, 10) and (– 4, 0)
(C) (0, 4) and (– 10, 0)
(D) (0, – 10) and (4, 0)
31. The ratio in which the point P (3/4, 5/12)divides the line segment joining the Points A (1/2, 3/2) and B (2, –5) is:
(A) 1:5
(B) 5:1
(C) 1:3
(D) 3:1
32. The points (- 1, – 2), (1, 0), (- 1, 2), (- 3, 0) forms a quadrilateral of type:
(a) Square
(b) Rectangle
(c) Parallelogram
(d) Rhombus
33. If the distance between the points A(2, -2) and B(-1, x) is equal to 5, then the value of x is:
(a) 2
(b) -2
(c) 1
(d) -1
34. The midpoints of a line segment joining two points A(2, 4) and B(-2, -4)
(a) (-2,4)
(b) (2,-4)
(c) (0, 0)
(d) (-2,-4)
35. The distance of point A(2, 4) from x-axis is
(a) 2 units
(b) 4 units
(c) -2 units
(d) -4 units
36. The distance between the points P(0, 2) and Q(6, 0) is
(a) 4√10
(b) 2√10
(c) √10
(d) 20
37 If O(p/3, 4) is the midpoint of the line segment joining the points P(-6, 5) and Q(-2, 3). The value of p is:
(a) 7/2
(b) -12
(c) 4
(d) -4
38. The point which divides the line segment of points P(-1, 7) and (4, -3) in the ratio of 2:3 is:
(a) (-1, 3)
(b) (-1, -3)
(c) (1, -3)
(d) (1, 3)
39.The ratio in which the line segment joining the points P(-3, 10) and Q(6, – 8) is divided by O(-1, 6) is:
(a) 1:3
(b) 3:4
(c) 2:7
(d) 2:5
40. The coordinates of a point P, where PQ is the diameter of a circle whose centre is (2, – 3) and Q is (1, 4) is:
(a) (3, -10)
(b) (2, -10)
(c) (-3, 10)
(d) (-2, 10)
41. The area of a rhombus if its vertices are (3, 0), (4, 5), (-1, 4) and (-2,-1) taken in order, is:
(a) 12 sq.units
(b) 24 sq.units
(c) 30 sq.units
(d) 32 sq.units
42. The distance of the point P(–6, 8) from the origin is
(a) 8 units
(b) 2√7 units
(c) 10 units
(d) 6 units
43 The distance between the points (0, 5) and (–5, 0) is
(a) 5 units
(b) 5√2 units
(c) 2√5 units
(d) 10 units
44. The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is
(a) 5
(b) 12
(c) 11
(d)
45 The area of a triangle with vertices (a, b + c), (b, c + a) and (c, a + b) is
(A) (a + b + c)2
(B) 0
(C) a + b + c
(D) ab
46. 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)
47. If the points A(1, 2), O(0, 0) and C(a, b) are collinear, then
(a) a = b
(b) a = 2b
(c) 2a = b
(d) a = –b
48. If the points A(6, 1), B(8, 2), C(9, 4) and D(p, 3) are the vertices of a parallelogram, taken in order, then the value of p is
(a) 4
(b) -6
(c) 7
(d) -2
49.. A line intersects the y-axis and x-axis at the points P and Q, respectively. If (2, -5) is the midpoint of PQ, then the coordinates of P and Q are, respectively
(a) (0, -5) and (2, 0)
(b) (0, 10) and (-4, 0)
(c) (0, 4) and (-10, 0)
(d) (0, -10) and (4, 0)
50. 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)
51 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)
52. 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) (11,2)
(d) (1, 3)
53. 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)
54. Two of the vertices of a ��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)
55. 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
56. Find the distance of the point (–6, 8) from the origin.
(a) 8
(b) 11
(c) 10
(d) 9
57. 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
58 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
59. 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
60. The vertices of a ΔABC and given by A(2, 3) and B(–2, 1) and its centroid is G (1,2/3) Find the coordinates of the third vertex C of the ΔABC.
a) (0, 2)
(b) (1, –2)
(c) (2, –3)
(d) (–2, 3)
62 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
63 The distance of the point P(2, 3) from the x-axis is
(a) 2
(b) 3
(c) 1
(d) 5
64.The distance between the points A(0, 6) and B(0, -2) is
(a) 6
(b) 8
(c) 4
(d) 2
65.The distance of the point P(-6, 8) from the origin is
(a) 8
(b) 2√7
(c) 10
(d) 6
66.The distance between the points (0, 5) and (-5, 0) is
(a) 5
(b) 5√2
(c) 2√5
(d) 10
67.AOBC is a rectangle whose three vertices are A(0, 3), O(0, 0) and B(5, 0). The length of its diagonal is
(a) 5
(b) 3
(c) 34−−√
(d) 4
68.The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is
(a) 5
(b) 12
(c) 11
(d) 7 + √5
69The 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
70.The points (-4, 0), (4, 0), (0, 3) are the vertices of a
(а) Right triangle
(b) Isosceles triangle
(c) Equilateral triangle
(d) Scalene triangle
71.The point which divides the lines segment joining the points (7, -6) and (3, 4) in ratio 1 : 2 internally lies in the
(a) I quadrant
(b) II quadrant
(c) III quadrant
(d) IV quadrant
72.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)
73.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)
74.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 = 1/4 AB
75.If P (α/3, 4) is the mid-point 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
76.The perpendicular bisector of the line segment joining the points A(l, 5) and B(4, 6) cuts the y-axis at
(a) (0, 13)
(b) (0, -13)
(c) (0, 12)
(d) (13, 0)
77.The coordinates of the point which is equidistant from the three vertices of the ΔAOB as shown in the figure.
a) (x, y)
(b) (y, x)
(c) (x2, y2)
(d) (y2, x2)
78.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)
79.A line intersects the y-axis and x-axis at the points P and Q respectively. If (2, -5) is the mid-point of PQ, then the coordinates of P and Q are respectively
(a) (0, -5) and (2, 0)
(b) (0, 10) and (-4, 0)
(c) (0, 4) and (-10, 0)
(d) (0, -10) and (4, 0)
80.The area of a triangle with vertices (a, b + c), (b, c + a) and (c, a + b) is
(a) (a + b + c)²
(b) 0
(c) a + b + c
(d) abc
81.If the distance between the points (4, P) and (1, 0) is 5, then the value of P is
(a) 4 only
(b) ± 4
(c) -4 only
(d) 0
82.If the points A(1, 2), O(0, 0), C(a, b) are collinear, then
(a) a = b
(b) a = 2b
(c) 2a = b
(d) a = -b
.1. The distance of the point P(2, 3) from the x-axis is
(a) 2
(b) 3
(c) 1
(d) 5
2. The distance between the point P(1, 4) and Q(4, 0) is
(a) 4
(b) 5
(c) 6
(d) 3√3
3. 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
4. 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
5. The distance of the point (α, β) from the origin is
(a) α + β
(b) α² + β²
(c) |α| + |β|
(d) root of α2+β2
6. 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
7. The line segment joining the points (3, -1) and (-6, 5) is trisected. The coordinates of point of trisection are
(a) (3, 3)
(b) (- 3, 3)
(c) (3, – 3)
(d) (-3,-3)
8. The line 3x + y – 9 = 0 divides the line joining the points (1, 3) and (2, 7) internally in the ratio
(a) 3 : 4
(b) 3 : 2
(c) 2 : 3
(d) 4 : 3
9. The distance between A (a + b, a – b) and B(a – b, -a – b) is
10. If (a/3, 4) is the mid-point of the segment joining the points P(-6, 5) and R(-2, 3), then the value of ‘a’ is
(a) 12
(b) -6
(c) -12
(d) -4
11. 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
12. The points (1,1), (-2, 7) and (3, -3) are
(a) vertices of an equilateral triangle
(b) collinear
(c) vertices of an isosceles triangle
(d) none of these
13. The coordinates of the centroid of a triangle whose vertices are (0, 6), (8,12) and (8, 0) is
(a) (4, 6)
(b) (16, 6)
(c) (8, 6)
(d) (16/3, 6)
14. Two vertices of a triangle are (3, – 5) and (- 7,4). If its centroid is (2, -1), then the third vertex is
(a) (10, 2)
(b) (-10,2)
(c) (10,-2)
(d) (-10,-2)
15. 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
16. 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
17. If the distance between the points (2, –2) and (–1, x) is 5, one of the values of x is
(A) –2
(B) 2
(C) –1
(D) 1
18.. 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)
19. The points A (9, 0), B (9, 6), C (–9, 6) and D (–9, 0) are the vertices of a
(A) Square
(B) Rectangle
(C) Rhombus
(D) Trapezium
20.. The distance of the point P (2, 3) from the x-axis is
(A) 2
(B) 3
(C) 1
(D) 5
21. The distance between the points A (0, 6) and B (0, –2) is
(A) 6
(B) 8
.22. AOBC is a rectangle whose three vertices are vertices A (0, 3), O (0, 0) and B (5, 0). The length of its diagonal is
(A) 5
(B) 3
(C) √34
(D) 4
23.. If P (a/3, 4) is the mid-point 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
.24 The coordinates of the point which is equidistant from the three vertices of the Δ AOB as shown in the figure is:
(A) (x, y)
(B) (y, x)
(C) (x/2, y/2)
(D) (y/2, x/2)
25. A circle drawn with origin as the centre passes through The point which does not lie in the interior of the circle is
(C) (5, –1/2)
(D) (–6, 5/2)
26. If the distance between the points (4, p) and (1, 0) is 5, then the value of p is
(A) 4 only
(B) ± 4
(C) – 4 only
(D) 0
27. 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
28. The point which divides the line segment joining the points (7, –6) and (3, 4) in ratio 1 : 2 internally lies in the
(A) I quadrant
(B) II quadrant
(C) III quadrant
(D) IV quadrant
29 One of the two points of trisection of the line segment joining the points A (7, – 2) and B (1, – 5) which divides the line in the ratio 1:2 are:
(A) (5, –3)
(B) (5, 3)
(C) (–5, –3)
(D) (13, 0)
30. A line intersects the y-axis and x-axis at the points P and Q, respectively. If (2, –5) is the mid - point of PQ, then the coordinates of P and Q are, respectively.
(A) (0, – 5) and (2, 0)
(B) (0, 10) and (– 4, 0)
(C) (0, 4) and (– 10, 0)
(D) (0, – 10) and (4, 0)
31. The ratio in which the point P (3/4, 5/12)divides the line segment joining the Points A (1/2, 3/2) and B (2, –5) is:
(A) 1:5
(B) 5:1
(C) 1:3
(D) 3:1
32. The points (- 1, – 2), (1, 0), (- 1, 2), (- 3, 0) forms a quadrilateral of type:
(a) Square
(b) Rectangle
(c) Parallelogram
(d) Rhombus
33. If the distance between the points A(2, -2) and B(-1, x) is equal to 5, then the value of x is:
(a) 2
(b) -2
(c) 1
(d) -1
34. The midpoints of a line segment joining two points A(2, 4) and B(-2, -4)
(a) (-2,4)
(b) (2,-4)
(c) (0, 0)
(d) (-2,-4)
35. The distance of point A(2, 4) from x-axis is
(a) 2 units
(b) 4 units
(c) -2 units
(d) -4 units
36. The distance between the points P(0, 2) and Q(6, 0) is
(a) 4√10
(b) 2√10
(c) √10
(d) 20
37 If O(p/3, 4) is the midpoint of the line segment joining the points P(-6, 5) and Q(-2, 3). The value of p is:
(a) 7/2
(b) -12
(c) 4
(d) -4
38. The point which divides the line segment of points P(-1, 7) and (4, -3) in the ratio of 2:3 is:
(a) (-1, 3)
(b) (-1, -3)
(c) (1, -3)
(d) (1, 3)
39.The ratio in which the line segment joining the points P(-3, 10) and Q(6, – 8) is divided by O(-1, 6) is:
(a) 1:3
(b) 3:4
(c) 2:7
(d) 2:5
40. The coordinates of a point P, where PQ is the diameter of a circle whose centre is (2, – 3) and Q is (1, 4) is:
(a) (3, -10)
(b) (2, -10)
(c) (-3, 10)
(d) (-2, 10)
41. The area of a rhombus if its vertices are (3, 0), (4, 5), (-1, 4) and (-2,-1) taken in order, is:
(a) 12 sq.units
(b) 24 sq.units
(c) 30 sq.units
(d) 32 sq.units
42. The distance of the point P(–6, 8) from the origin is
(a) 8 units
(b) 2√7 units
(c) 10 units
(d) 6 units
43 The distance between the points (0, 5) and (–5, 0) is
(a) 5 units
(b) 5√2 units
(c) 2√5 units
(d) 10 units
44. The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is
(a) 5
(b) 12
(c) 11
(d)
45 The area of a triangle with vertices (a, b + c), (b, c + a) and (c, a + b) is
(A) (a + b + c)2
(B) 0
(C) a + b + c
(D) ab
46. 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)
47. If the points A(1, 2), O(0, 0) and C(a, b) are collinear, then
(a) a = b
(b) a = 2b
(c) 2a = b
(d) a = –b
48. If the points A(6, 1), B(8, 2), C(9, 4) and D(p, 3) are the vertices of a parallelogram, taken in order, then the value of p is
(a) 4
(b) -6
(c) 7
(d) -2
49.. A line intersects the y-axis and x-axis at the points P and Q, respectively. If (2, -5) is the midpoint of PQ, then the coordinates of P and Q are, respectively
(a) (0, -5) and (2, 0)
(b) (0, 10) and (-4, 0)
(c) (0, 4) and (-10, 0)
(d) (0, -10) and (4, 0)
50. 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)
51 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)
52. 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) (11,2)
(d) (1, 3)
53. 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)
54. Two of the vertices of a ��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)
55. 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
56. Find the distance of the point (–6, 8) from the origin.
(a) 8
(b) 11
(c) 10
(d) 9
57. 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
58 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
59. 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
60. The vertices of a ΔABC and given by A(2, 3) and B(–2, 1) and its centroid is G (1,2/3) Find the coordinates of the third vertex C of the ΔABC.
a) (0, 2)
(b) (1, –2)
(c) (2, –3)
(d) (–2, 3)
62 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
63 The distance of the point P(2, 3) from the x-axis is
(a) 2
(b) 3
(c) 1
(d) 5
64.The distance between the points A(0, 6) and B(0, -2) is
(a) 6
(b) 8
(c) 4
(d) 2
65.The distance of the point P(-6, 8) from the origin is
(a) 8
(b) 2√7
(c) 10
(d) 6
66.The distance between the points (0, 5) and (-5, 0) is
(a) 5
(b) 5√2
(c) 2√5
(d) 10
67.AOBC is a rectangle whose three vertices are A(0, 3), O(0, 0) and B(5, 0). The length of its diagonal is
(a) 5
(b) 3
(c) 34−−√
(d) 4
68.The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is
(a) 5
(b) 12
(c) 11
(d) 7 + √5
69The 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
70.The points (-4, 0), (4, 0), (0, 3) are the vertices of a
(а) Right triangle
(b) Isosceles triangle
(c) Equilateral triangle
(d) Scalene triangle
71.The point which divides the lines segment joining the points (7, -6) and (3, 4) in ratio 1 : 2 internally lies in the
(a) I quadrant
(b) II quadrant
(c) III quadrant
(d) IV quadrant
72.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)
73.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)
74.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 = 1/4 AB
75.If P (α/3, 4) is the mid-point 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
76.The perpendicular bisector of the line segment joining the points A(l, 5) and B(4, 6) cuts the y-axis at
(a) (0, 13)
(b) (0, -13)
(c) (0, 12)
(d) (13, 0)
77.The coordinates of the point which is equidistant from the three vertices of the ΔAOB as shown in the figure.
a) (x, y)
(b) (y, x)
(c) (x2, y2)
(d) (y2, x2)
78.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)
79.A line intersects the y-axis and x-axis at the points P and Q respectively. If (2, -5) is the mid-point of PQ, then the coordinates of P and Q are respectively
(a) (0, -5) and (2, 0)
(b) (0, 10) and (-4, 0)
(c) (0, 4) and (-10, 0)
(d) (0, -10) and (4, 0)
80.The area of a triangle with vertices (a, b + c), (b, c + a) and (c, a + b) is
(a) (a + b + c)²
(b) 0
(c) a + b + c
(d) abc
81.If the distance between the points (4, P) and (1, 0) is 5, then the value of P is
(a) 4 only
(b) ± 4
(c) -4 only
(d) 0
82.If the points A(1, 2), O(0, 0), C(a, b) are collinear, then
(a) a = b
(b) a = 2b
(c) 2a = b
(d) a = -b
Q.1. 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)
Answer
Q.2. The distance of the point P(-6,8) from the origin is
(a) 8
(b) 2√7
(c) 6
(d) 10
Answer
Q.3. If R(5,6) is the midpoint of the line segment AB joining the points A(6,5) and B(4,y) then y equals
(a) 5
(b) 7
(c) 12
(d) 6
Answer
Q.4. 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
Answer
Q.5. The distance of the point (-3, 4) from x-axis is
(a) 3
(b) -3
(c) 4
(d) 5
Answer
Q.6. The perimeter of the triangle with vertices (0,4), (0,0) and (3,0) is
(a) 7 + √5
(b) 5
(c) 10
(d) 12
Answer
Q.7. 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
Answer
Q.8. 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)
Answer
Q.9. 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
Answer
Q.10. 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
Answer
Q.11. The coordinates of the point P dividing the line segment joining the points A(1,3), and B(4,6) in the ratio 2:1 is
(a) (2,4)
(b) (3,5)
(c) (4,2)
(d) (5,3)
Answer
Q.12. 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)
Answer
Q.13. 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
Answer
Q.14. 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
Answer
Q.15. 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)
(a) (0,2)
(b) (2,0)
(c) (3,0)
(d) (0,3)
Answer
Q.2. The distance of the point P(-6,8) from the origin is
(a) 8
(b) 2√7
(c) 6
(d) 10
Answer
Q.3. If R(5,6) is the midpoint of the line segment AB joining the points A(6,5) and B(4,y) then y equals
(a) 5
(b) 7
(c) 12
(d) 6
Answer
Q.4. 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
Answer
Q.5. The distance of the point (-3, 4) from x-axis is
(a) 3
(b) -3
(c) 4
(d) 5
Answer
Q.6. The perimeter of the triangle with vertices (0,4), (0,0) and (3,0) is
(a) 7 + √5
(b) 5
(c) 10
(d) 12
Answer
Q.7. 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
Answer
Q.8. 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)
Answer
Q.9. 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
Answer
Q.10. 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
Answer
Q.11. The coordinates of the point P dividing the line segment joining the points A(1,3), and B(4,6) in the ratio 2:1 is
(a) (2,4)
(b) (3,5)
(c) (4,2)
(d) (5,3)
Answer
Q.12. 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)
Answer
Q.13. 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
Answer
Q.14. 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
Answer
Q.15. 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)
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