AP 10th Maths Mock Test 2021 for Chapter-7 "Coordinate Geometry" Online Practice Test

1. If $A = (a^{2}, 2a); B = (\frac{1}{ a^{2}} , -\frac{2}{a} )$ and $S = (1, 0)$ then $\frac{1}{SA} + \frac{1}{SB}$ =

-3

-2

2. If $(0, 0), (3, \sqrt{3})$ and $(3, k)$ forms an equilateral triangle, then the value of 'k' is

$-\sqrt{3}$

$\sqrt{3}$

$\sqrt{2}$

$2\sqrt{3}$

3. If the line $3x +4y = 24$ cuts the x – axis at A and y – axis at B, then the area of $\bigtriangleup AOB$ is ____ sq. units

4. The points $A(0,\frac{8}{3} ) , B(1, 3) , C(82, 30)$ are

Vertices of a right angled triangle

Vertices of an equilateral triangle

Vertices of right angled isosceles triangle

None

5. If A and B are the points (-3, 4) and (2, 1) respectively, then the coordinates of the point C on AB produced such that $AC = 2BC$ are

(5 , -1)

(1 , -2)

(7 , -2)

(0 , -1)

6. The area of the triangle with vertices $(a, b + c), (b, c + a)$ and $(c, a + b)$ is ___ sq.units.

$\frac{1}{2}$

7. If the distance of the point $(4, a)$ from x – axis is half its distance from y – axis, then value of 'a' is

8. If four vertices of a parallelogram taken in order $(-3, -1), (a, b), (3, 3)$ and $(4, 3)$ , then $a : b$ =

1 : 2

4 : 1

1 : 3

4 : 5

9. Radius of circumcircle of a triangle ABC is $5\sqrt{10}$ units. If point 'P' is equidistant from $A (1, 3), B (-3, 5)$ and $C (5, -1)$ then $AP$ = ____ units

$\sqrt{10}$

$5\sqrt{10}$

$\sqrt{2}$

10. The line formed by joining $(-1, 1)$ and $(5, 7)$ is divided by a line $x + y = 4$ in the ratio of

1 : 3

3 : 5

2 : 3

1 : 2

11. The ratio in which the line $3x + 4y = 9$ divides the join of $(1, 3)$ and $(2, 7)$ is

1 : 3

2 : 5

6 : 25 externally

6 : 11 externally

12. The coordinates of the midpoint of the line joining the points $(3p, 4)$ and $(-2, 2q)$ are $(5, p)$ , then the values of 'p' and 'q' respectively are

3 and -1

1 and 2

4 and 2

-4 and 5

13. If the points $(x, y), (-5, -2)$ and $(3, -5)$ are collinear, then the relation between 'x' and 'y' is

3x + 8y + 31 = 0

x + 3y + 11 = 0

3x + 4y + 11 = 0

2x – 3y + 15 = 0

14. 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

$\frac{7}{2}$

15. If the points $(p, q), (m, n)$ and $(p - m, q - n)$ are collinear then $\frac{p}{q}$ =

$mn$

$m^{2} + n^{2}$

$m + n$

$\frac{m}{n}$

16. If $P (9a - 2, -b)$ divides the line segment joining $A (3a + 1, -3)$ and $B (8a , 5)$ in the ratio $3 : 1$ , then the value of $2a + b$ =

-1

17. The centre of a circle is $(2a, a - 7)$ . If the circle passes through the point $(11, -9)$ and has a diameter $10\sqrt{2}$ units, then the value of ‘a’ is

5 or 3

2 or 5

-1 or 2

3 or 7

18. If the midpoint of the line joining $(3, 4)$ and $(k, 7)$ is $(x, y)$ and $2x + 2y + 1 = 0$ , then the value of 'k' is

-15

19. The value of 'x' for which the distance between $(-2, 5)$ and $(x, 19)$ will be $\sqrt{205}$ units is

-1

20. Point P divides the line segment joining the points $A (2, 1)$ and $B (5, -8)$ such that $\frac{AP}{PB} = \frac{1}{3}$ . If 'p' lies on $2x - y + k = 0$ , then the value of 'k' is

-8

21. If $(6, 6), (0, 6)$ and $(6, 0)$ are the vertices of a triangle, then the distance between circumcentre and centroid is ___ units.

$\sqrt{2}$

$2\sqrt{2}$

$\sqrt{3}$

22. If $A (-1, -3), B (-1, 4), C (5, -3)$ are the vertices of a triangle, then the orthocentre of that triangle is

(1 , -2)

(0 , -3)

(-1 , -3)

(-1 , 0)

23. If the point 'P' is equidistant to $A (1, 3), B (-3, 5)$ and $C (5, -1)$ the $PA$ =

$\sqrt{10}$

$\sqrt{5}$

$5\sqrt{10}$

24. If $(0, 0), (5, 12)$ and $(16, 12)$ are the vertices of a triangle, then the incentre of that triangle is

(1 , 3)

(7 , 9)

(-1 , 9)

(7 , 0)

25. If $A (6, 3), B (3, 5), C (4, 2), P (\alpha , \beta)$ are four points in a plane, then ratio of areas of $\bigtriangleup PBC$ and $\bigtriangleup ABC$ is

$(3\alpha + \beta - 14) : 7$

$(\alpha + \beta) : 7$

$(2\alpha + \beta - 11) : 7$

$\alpha : 7$

26. The orthocentre and circumcentre of a triangle are $(2, -3)$ and $(5, 6)$ respectively, then its centroid is

(1 , 3)

(2 , 3)

(4 , 3)

(-1 , 5)

27. If $A (2, -5), B (2, 7)$ and $C (4, 7)$ are the vertices of a triangle, then its circumcentre is

(1 , 3)

(3 , 1)

(1 , 0)

(-1 , 5)

28. If $A (3, 7), B (3, -2)$ and $C (5, 7)$ are the vertices of a triangle, then its circumradius is

$\sqrt{35}$ units

$\sqrt{17}$ units

$\frac{\sqrt{65}}{2}$ units

$\frac{\sqrt{85}}{2}$ units

29. $A (-9, 0)$ and $B (-1, 0)$ are two points such that $PA : PB = 3 : 1$ where $P (x, y)$ is a point in that plane, then

$x + y = 9$

$x^{2} + y^{2} = 11$

$x^{2} + y^{2} + xy = 0$

$x^{2} + y^{2} = 9$

30. $A (2, 3), B (3, -4)$ and $P (x, y)$ are such that $PA^{2} +PB^{2} = 10$ then the relation between 'x' and 'y' is

$x^{2} + y^{2} - 5x + y + 14 = 0$

$x^{2} + y^{2} - 5x + y = 0$

$x^{2} + y^{2} - x - y - 14 = 0$

None

31. The angle between two lines, whose slopes are $\frac{3}{4}$ and $-\frac{1}{7}$ is

$\frac{\pi}{2}$

$\frac{\pi}{3}$

$\frac{\pi}{4}$

$\frac{\pi}{6}$

32. The angle between two lines, whose slopes are $\frac{3}{2}$ and $-\frac{2}{3}$ is

$\frac{\pi}{4}$

$\frac{\pi}{2}$

$\frac{\pi}{5}$

$\frac{\pi}{6}$

33. The area of the triangle formed by the lines $x = 0, y = 0$ and $3x + 4y = 12$ is _ sq.units.

34. The perpendicular distance from origin to a straight line, whose intercepts on coordinates axes are 4, -3 respectively is ___ units.

$\frac{12}{5}$

$\frac{13}{5}$

35. The perpendicular distance between the point $(1, 2)$ to the line $12x + 5y = 7$ is__ units

$\frac{15}{12}$

$\frac{15}{13}$

$\frac{5}{3}$

$\frac{11}{15}$

36. The distance between two parallel lines $4x + 3y + 7 = 0$ and $12x + 9y + 1 = 0$ is

$\frac{4}{3}$

$\frac{2}{3}$

$\frac{5}{3}$

$\frac{3}{2}$

37. If the point $(4, 2)$ divides the join of $(5, -1)$ and $(2, y)$ in the ratio $1 : 2$ then the value of 'y' is

38. The point of trisection of the line segment joining the points $(5, -6)$ and $(-7, 5)$ is

$(0 , -1)$ and $(-1 , \frac{4}{3} )$

$(1 , \frac{3}{5})$ and $(5 , -\frac{4}{3} )$

$(1 , -\frac{7}{3})$ and $(-3 , \frac{4}{3} )$

None

39. If the three vertices of a parallelogram are $A(3, -4), B(-1, -3)$ and $C(-6, 2)$ , then the area of parallelogram $ABCD$ is ____ sq.units.

$\frac{15}{2}$

40. The points $(5, -2), (6, 4)$ and $(7, -2)$ forms

An equilateral triangle

Right angled triangle

An isosceles triangle

Scalene triangle

41. If $Q(0, 1)$ is equidistant from $P(5, -3)$ and $R(x, 6)$ then the length of $PR$ = ___ units.

$\sqrt{2}$

$9\sqrt{2}$

$3\sqrt{2}$

42. The points $(0, a), (\frac{b}{2} , \frac{a}{2})$ and $(b, 0)$ are

Collinear

Coincident

Collinear & Coincident

None

43. The points $(a, -a), (-a, -a)$ and $(-a\sqrt{3}, a\sqrt{3})$ forms

An isosceles triangle

Scalene triangle

An equilateral triangle

Right angled triangle

44. If the line segment joining the points $(3, -4)$ and $(1,2)$ is trisected at the points $P(p, -2)$ and $Q(\frac{5}{3}, q)$ respectively. Then $p + q$ =

$\frac{5}{3}$

$\frac{7}{3}$

$\frac{1}{3}$

45. The distance between the points $P(\frac{sin \theta }{2}, 0)$ and $Q(0 , \frac{cos \theta }{2})$ is

-5

$\frac{1}{3}$

$\frac{1}{2}$

46. The area of triangle formed with the vertices $A(at_{1} ^{2} , 2at_{1}), B(at_{2} ^{2} , 2at_{2})$ and $C(at_{3} ^{2} , 2at_{3})$ is ___ sq.units

$a^{2} \mid(t_{1} - t_{2} )( t_{2} - t_{3} )( t_{3} - t_{1} ) \mid$

$a^{2} \mid(t_{1}t_{2}t_{3}\mid$

$a \mid(t_{1} - t_{2} )( t_{3} - t_{1} ) \mid$

47. The area of triangle formed with the vertices $A(a, c + a), B(a, c)$ and $C(-a, c - a)$ is

$a$ sq.units

$a^{2}$ sq.units

$\sqrt{a}$ sq.units

$a^{3}$ sq.units

48. The distance between the points $A(10 cos \theta, 0)$ and $B(0, 10 sin \theta)$ is ___ units.

$\sqrt{10}$

$\sqrt{5}$

49. The distance between $(5 sin 60^{0}, 0)$ and $(0, 5 sin 30^{0})$ is ____ units.

$\frac{5}{2}$

$\frac{3}{2}$

50. If the centroid of the triangle formed by the points $P(a,b), Q(b, c)$ and $R(c, a)$ is at the origin, the value of $a + b + c$ is

51. If the centroid of the triangle formed by the points $P(a,b), Q(b, c)$ and $R(c, a)$ is at the origin, the value of $\frac{ a^{2} }{bc} + \frac{ b^{2} }{ac} + \frac{ c^{2} }{ab}$ is

-3

52. If the mid-point of the segment joining $A(x, y + 1)$ and $B(x + 1, y + 2)$ is $C(\frac{3}{2} , \frac{5}{2})$ then $x^{2} + y^{2}$ =

-5

53. The area of quadrilateral ABCD whose vertices are $A(1, 1), B(7, -3), C(12, 2)$ and $D(7, 21)$ respectively is ___ sq.units.

$\frac{132}{5}$

132

54. If the point of intersection of $2x + 3y = 11$ and $2x - 4y = -24$ satisfies the equation $y = mx + 3$ , the value of 'm' is

-1

-3

55. The distance between the points $(a cos \alpha, a sin \alpha)$ and $(a cos \beta, a sin \beta)$ is __ units.

$a(\frac{ \alpha - \beta }{2})$

$2a\mid sin(\frac{ \alpha - \beta }{2}) \mid$

$2a(\alpha - \beta)$

None

56. If the distance between the points $(a, 2)$ and $(3, 4)$ is $2\sqrt{2}$ , then the value of ‘a’ is

0 or -1

1 or 5

-1 or -5

-1 or -3

57. If $3x + 7y -1 = 0$ and $7x - py + 3 = 0$ are perpendicular to each other, then the value of ‘p’ is

-4

58. If the slope of the line passing through $(2, 5)$ and $(k, 3)$ is 2, then the value of 'k' is

-1

$\frac{1}{2}$

59. If $6x - 10y + 3 = 0$ and $ax - 5y + 8 = 0$ are parallel to each other, then the value of ‘a’ is

$\frac{1}{3}$

$\frac{2}{5}$

-3

60. Midpoint of the line segment joining the points $A(cosec^{2} \alpha , sin^{2} \alpha)$ and $B(-cot^{2} \alpha , cos^{2} \alpha)$ is

(1 , 1)

(2 , 2)

$(\frac{1}{2} , \frac{1}{2})$

$(\frac{1}{3} , \frac{1}{3})$

61. The ratio in which x-axis divides the join of $(3, 6)$ and $(12, -3)$ is

1 : 3

2 : 1

3 : 5

1 : 5

62. The ratio in which y-axis divides the join of $(-3, 4)$ and $(1, -2)$ is

3 : 5

3 : 1

1 : 2

2 : 1

63. The centroid of a triangle with vertices $(sec^{2} \theta , cosec^{2} \theta), (-tan^{2} \theta , -cot^{2} \theta)$ and $(1, 1)$ is

$( \frac{1}{3} , \frac{1}{3} )$

$( \frac{1}{2} , \frac{1}{2} )$

$(1 , 1)$

$( \frac{2}{3} , \frac{2}{3} )$

64. The sum of the squares of the intercepts made by the line $2x + 3y + 13 = 0$ with x-axis and y-axis is

$\frac{197}{36}$

$\frac{137}{36}$

$\frac{2197}{36}$

$\frac{2197}{16}$

65. If the angle between $5x + 3y - 2 = 0$ and $3x - ky + 3 = 0$ is a right angle, then the value of 'k' is

-5

-3

66. The area of the triangle formed by the line $2x - 4y - 7 = 0$ with the coordinate axes is __ units.

$\frac{49}{8}$

$\frac{49}{16}$

$\frac{29}{16}$

$\frac{48}{9}$

67. The coordinates of the point which divides the join of $A(2, -4)$ and $B(5, 6)$ externally in the ratio $5 : 3$ is

$(\frac{19}{2} , 21)$

$(\frac{9}{2} , 11)$

$(-\frac{19}{2} , -21)$

$(9 , -3)$

68. Distance between the parallel lines $5x - 3y - 4 = 0$ and $10x - 6y - 9 = 0$ is __ units.

$\sqrt{136}$

$\frac{1}{ \sqrt{112} }$

$\frac{1}{ \sqrt{136} }$

69. The distance between the point $(2, 3)$ to the line $4x - 5y + 3 = 0$ is __ units

$\sqrt{41}$

$\frac{2}{ \sqrt{21} }$

$\frac{4}{ \sqrt{41} }$

$\frac{4}{ \sqrt{61} }$

70. The distance between the origin $O(0, 0)$ to the line $2x - 4y - 7 = 0$ is __ units

$\frac{5}{ \sqrt{10} }$

$\frac{7}{ \sqrt{20} }$

$\frac{1}{ \sqrt{20} }$

$\sqrt{20}$

71. If $D(2, 1), E(4, 5)$ and $F(-1, -3)$ are the points of the sides of $\bigtriangleup ABC$ , then the coordinates of vertex 'B' are

(-3 , -7)

(1 , 7)

(3 , -1)

(1 , -7)

72. If $(k, 2k), (2k, 3k)$ and $(3, 1)$ are collinear to each other, then the value of 'k' is

-2

-1

73. The angle made by the line joining $(-1, 0)$ and $(-2, -\sqrt{3})$ with the positive direction of x-axis is __ degrees.

74. The condition that $a_{1} x + b_{1} y + c_{1} = 0$ and $a_{2} x + b_{2} y + c_{2} = 0$ are perpendicular to each other is

$a_{1} = a_{2}$

$a_{1} = b_{2}$

$a_{1} a_{2} + b_{1} b_{2} = 0$

$a_{1} a_{2} - b_{1} b_{2} = 1$

75. The centroid of the triangle whose sides are $x = 0, y = 0$ and $x + y = 6$ is

(1 , 1)

(2 , 2)

(3 , 3)

(6 , 6)

76. The angle between the straight lines $4x - y + 7 = 0$ and $3x - 5y - 9 = 0$ is __ degrees.

77. If $(a + b, a - b), (2a + b, 2a - b)$ and $(a - b, a + b)$ are three consecutive vertices of a parallelogram, then the coordinates of the fourth vertex is

(-b , b)

(a , b)

(b , -1)

(1 , -b)

78. Slope of the line joining $(-a, a)$ and $(0, a + a\sqrt{3})$ is

$\sqrt{3}$

$\sqrt{2}$

$2\sqrt{3}$

79. The angle subtended by the origin by the line segment whose endpoints are $(0, 10)$ and $(10, 0)$ is ___ degrees.

80. The ratio in which the line $x - y - 2 = 0$ divides the line segment joining the points $(3, -1)$ and $(8, 9)$ is

1 : 2

2 : 3

1 : 3

3 : 5

81. The value of 'y', if $(\frac{23}{5}, y)$ divides the line segment joining the points $(5, 7)$ and $(4, 5)$ internally in the ratio $2 : 3$ is

$\frac{31}{5}$

82. If the point $P(2, 1)$ lies on the line segment joining the points $A(4, 2)$ and $B(8, 4)$ , then the relation between $AP$ and $AB$ is

$AP = 2AB$

$AP = \frac{1}{2}AB$

$AB = \frac{1}{2}AP$

$AP = \frac{1}{3}AB$

83. The ratio that $C(\frac{3}{5} , \frac{11}{5})$ divide the line segment joining the points $A(3, 5)$ and $B(-3, -2)$ is

1 : 2

3 : 1

2 : 3

2 : 1

84. If two adjacent vertices of a parallelogram are $(3, 2)$ and $(-1, 0)$ and the diagonals intersect at $(2, -5)$ , then the other two vertices are

(1, -12) and (5, -10)

(1, -10) and (2, -3)

(1, -11) and (5, -5)

None

85. If $A(-6, 10), B(-4, 6)$ and $C(3, -8)$ are three points then $9AB$ =

3AC

2AC

4AC

86. If $(a, a), (-a, -a)$ and $(-\sqrt{3}a, \sqrt{3}a)$ are the vertices of an equilateral triangle, then the height of the triangle is __ units.

$\sqrt{6}a$

$\sqrt{3}a$

$6a$

$\sqrt{2}a$

87. If $(8, 6), (8, -2)$ and $(2, -2)$ are the vertices of a triangle, then the coordinates of the circumcentre of the triangle is

(-1, -5)

(5, 2)

(2, -5)

(-1, -3)

88. The ratio in which the point $P(\frac{3}{4} , \frac{5}{12})$ divides the line segment joining the points $A(-\frac{1}{2} , \frac{3}{2})$ and $B(2, -5)$ is

1 : 2

1 : 3

1 : 4

1 : 5

89. If $D(-\frac{1}{2} , \frac{5}{2}), E(7, 3)$ and $F(\frac{7}{2} , \frac{7}{2})$ are the midpoints of sides of $\bigtriangleup ABC$ , then the area of $\bigtriangleup ABC$ is ___ sq.units

5.5

3.5

90. If two vertices of an equilateral triangle are $(0,0)$ and $(3, \sqrt{3})$ then co-ordinates of the third vertex are

$(3 , -\sqrt{3})$

$(0 , 2\sqrt{3})$

$(3, -\sqrt{3})$ , $(0 , 2\sqrt{3})$

$(2 , -2\sqrt{3})$

91. Distance of $(2 + \sqrt{3}, 2 - \sqrt{3})$ from the origin is ___ units

$\sqrt{10}$

$\sqrt{14}$

$\sqrt{7}$

$\sqrt{3}$

92. The distance between $P(b + c, c + a)$ and $Q(c + a, a + b)$ is

$\sqrt{ a^{2} +2b^{2} + c^{2} - 2ab - 2bc }$

$a^{2} +2b^{2} + c^{2}$

$a + 2b + c$

$\sqrt{ a^{2} +2b^{2} + c^{2} - ab - bc -ca }$

93. The triangle formed with the vertices $(1, -1), (-\frac{1}{2} , \frac{1}{2})$ and $(1, 2)$ is

Scalene triangle

Isosceles triangle

Equilateral triangle

Right angled triangle

94. Area of a quadrilateral with vertices $(1, 1), (3, 4), (5, -2)$ and $(4, -7)$ is __ sq.units

12.5

$\frac{31}{2}$

$\frac{41}{2}$

95. If the area formed by the points $A(1, 2), B(-5, 6), C(7, -4)$ and $D(k, -2)$ taken in order is zero, then the value of 'k' is

-1

96. The centre of the circle passing through the points $(6, -6), (3, -7)$ and $(3, 3)$ is

(1, -1)

(3, -2)

(-2, 3)

(0, 1)

97. The length of the altitude through A, where $A(5,1), B(2, 4)$ and $(-1, -1)$ are the vertices of $\bigtriangleup ABC$ is

$\frac{24}{ \sqrt{34}}$

$\frac{12}{ \sqrt{10}}$

$8\sqrt{3}$

$4\sqrt{2}$

98. The area of the triangle formed by the midpoints of sides of the triangle whose vertices are $(2, 1), (-2, 3)$ and $(4, -3)$ is __ sq.units.

1.5

$\frac{3}{ \sqrt{2}}$

3.5

99. If the points $A(4, 3)$ and $B(x, 5)$ are on the circle with centre $O(2, 3)$ , then the value of $x^{2} + 5$ is ___ units.

$\frac{9}{2}$

100. If $(a, b)$ is the midpoint of the line segment joining the points $(5, 7)$ and $(3, 9)$ and $(x, y)$ is the midpoint of the line segment joining the points $(8, 6)$ and $(0, 10)$ then the value of $xa + yb$ is

101. If $(2, 4), (2, 6)$ are two vertices of an equilateral triangle, then the third vertex is

$( \sqrt{3} , 5 )$

$( 3 , \sqrt{3} )$

$( 2 + \sqrt{3} , 5 )$

$( 1 + \sqrt{3} , 5 )$

102. If $(2, 1), (4, 3), (-2, 5)$ are the three vertices of a square in order then the fourth vertex is

(-4, 3)

(3, -1)

(-1, -2)

103. The adjacent vertices of a square are $(1, 2)$ and $(3, 4)$ , then the length of its sides is __ units.

$\sqrt{2}$

$2\sqrt{2}$

$2\sqrt{3}$

$\sqrt{3}$

104. If $3x + y + 2 = 0, 2x - y - 3 = 0$ and $2x + ay - 6 = 0$ are concurrent lines then the value of ‘a’ is

105. If the point of intersection of $kx + 4y + 2 = 0$ and $x - 3y + 5 = 0$ lie on $2x + 7y - 3 = 0$ , then the value of 'k' is

106. If $(1, 2), (3, 4), (2, 1)$ and $(-1, -2)$ are the vertices of a square, then the point of intersection of its diagonal is

$(7, 8)$

$(-\frac{1}{5} , \frac{3}{5})$

$(\frac{7}{5} , \frac{8}{5})$

$(\frac{6}{5} , -\frac{3}{8})$

107. The distance of the point $(5, -2)$ from x-axis is ___ unit

$2\sqrt{2}$

108. The distance of the point $(-2, 5)$ from y-axis is __ units.

$\sqrt{2}$

109. The angle between x-axis and y-axis is __ degrees

110. Point of intersection of $2x + 3y + 4 = 0$ and $6x - y + 12 = 0$ is

(-1, 2)

(-2, 3)

(-2, 0)

(-1, 0)

111. The ratio with which x-axis divides the join of $(2, -3)$ and $(5, 7)$ is

1 : 3

3 : 7

3 : 5

6 : 7

112. A, B, C are collinear. $A = (3, 4); B = (7, 7)$ and $AC = 10$ . Then the coordinates of 'C' are

(5, 2)

(-5, -2)

(-5, 0)

(-1, -3)

113. The coordinates of centroid of a triangle with vertices $A(1, 2), B(4, -3)$ and $C(-2, 4)$ are

(1, 3)

(0, 3)

(1, 1)

(-1, -2)

114. The coordinates of centroid of a triangle are $(1, 4)$ . Two vertices of the triangle are $(4, -3), (-9, 7)$ . Then the area of that triangle is ___ sq.units

$\frac{183}{2}$

183

115. The area of a triangle with vertices $(t, 2t), (-2, 6)$ and $(3, 1)$ is 5 sq.units. Then the value of ‘t’ is

2 or $\frac{2}{3}$

1 or $-\frac{1}{3}$

-2 or $\frac{2}{5}$

None

116. If $(k, 2 - 2k), (- k + 1, 2k)$ and $(- 4 - k, 6 - 2k)$ are collinear, then the value of 'k' is

-3 or 2

-2 or $\sqrt{2}$

-1 or $\frac{1}{2}$

-1 and 3

117. The triangle with vertices $(-2, 1), (2, -2)$ and $(5, 2)$ is

Equilateral triangle

Scalene triangle

Right triangle

Isosceles triangle

118. Angle made by the line $y = x$ with the positive direction of x-axis is __ degrees.

135

119. The slope of a line parallel to $3x - by + 7 = 0$ is -3. Then the value of 'b' is

-1

-3

120. If $P = (6, -1), Q = (1, 3), R = (x, 8)$ , such that $PQ = QR$ , then the value of 'x' is

-1

121. Distance between the points $(at_{1} ^{2} , 2at_{1})$ and $(at_{2} ^{2} , 2at_{2})$ is

$a( t_{1} - t_{2} ) + t_{1} ^{2} + t_{2} ^{2}$

$a( t_{1} - t_{2} )\sqrt{ ( t_{1} + t_{2} )^{2} + 4}$

$t_{1} - t_{2}$

$\sqrt{t_{1} - t_{2}}$

122. The point that is equidistant to $(7, 6)$ and $(-3, 4)$ on x-axis is

(3, 0)

(-3, -5)

(0, -3)

(0, 3)

123. If the segment joining the points $(a, b)$ and $(c, d)$ subtends a right angle at the origin, then

$ac + bd = 1$

$ac + bd = -1$

$ac + bd = 0$

$ab + cd = 0$

124. If the origin is the midpoint of the line segment joined by the points $(2, 3)$ and $(x, y)$ then the value of $x + y$ is

-5

$-\frac{5}{2}$

$-\frac{3}{2}$

125. The perimeter of a triangle with vertices $(0, 4), (0, 0)$ and $(3, 0)$ is

126. The perpendicular bisector of the line segment joining the points $A(1, 5)$ and $B(4, 6)$ cuts the y-axis at

(1, 13)

(1, 5)

(-1, -5)

(0, 13)

127. If the distance between the points $(4, p)$ and $(1, 0)$ is 5, then the value of 'p' is

$\pm2$

$\pm6$

$\pm4$

$\pm1$

128. The ratio in which the point $P(m, 6)$ divides the join of $A(-4, 3)$ and $B(2, 8)$ is

3 : 2

1 : 3

1 : 2

2 : 5

129. The distance between the points $(a cos 35^{0}, 0)$ and $(0, a cos 65^{0})$ is

$a^{2}$

$\sqrt{a}$

130. The relation between 'x' and 'y' if $(x, y)$ is equidistant from the points $(7, 1)$ and $(3, 5)$ is

$x + y = 1$

$x - y = 3$

$x - y = 2$

$x - y = 4$

131. The value of ‘b’, if $P(b,1)$ divides the join of $A(7, -2)$ and $B(-5, 6)$ in the ratio $3 : 5$ is

$\frac{5}{2}$

$5$

$\frac{2}{5}$

$\frac{ \sqrt{5} }{2}$

132. The co-ordinates of the midpoint of the line joining the points $(3p, 4)$ and $(-2, 2q)$ are $(5, p)$ . Then $p - q$ =

-2

-3

133. If $(-1, 3), (2, p)$ and $(5, -1)$ are collinear, then the value of 'p' is

-1

134. If $(-2, -1), (a, 0), (4, b)$ and $(1, 2)$ are the vertices of a parallelogram, then the values of 'a' and 'b' respectively are

-1 , 5

-1 , -2

1 , 5

1 , 3

135. The points $A(1, 2), B(5, 4), C(3, 8)$ and $D(-1, 6)$ forms a

Square

Rectangle

Parallelogram

Trapezium

136. One of the co-ordinates of point of trisection of the line segment joining $(1, -2)$ and $(-3, 4)$ is

$(-1 , 0)$

$(-3 , 0)$

$(-\frac{1}{3} , 0)$

$(0 , -\frac{2}{3})$

137. If the points $A(4, 3)$ and $B(x, 5)$ are on the circle with centre $O(2, 3)$ , then the value of 'x' is

-5

138. If $A(5, 1), B(1, 5)$ and $(-3, -1)$ are the vertices of $\bigtriangleup ABC$ and D is the midpoint of $BC$ , then length of the median $AD$ is __ units.

$\sqrt{17}$

$\sqrt{37}$

$\sqrt{35}$

$\sqrt{74}$

139. If the points $(0, 0), (a, 0)$ and $(0, b)$ are collinear, then

$a = b$

$a \neq b$

$ab = 0$

$a + b = 0$

140. The area of the triangle whose vertices are $(-5, -1), (3, -5)$ and $(5, 2)$ is __ sq.units

141. The three vertices of a parallelogram taken in order are $(1, 2), (2, 4)$ and $(3, 7)$ . Then fourth vertex of that parallelogram is

(2, 5)

(1, 3)

(-2, -5)

(-5, 0)

142. The coordinates of the point, dividing the join of $(5, 0)$ and $(0, 4)$ internally in the ratio $2 : 3$ is

$(1, \frac{5}{8})$

$(3, \frac{8}{5})$

$(-2, \frac{8}{5})$

$(0, -\frac{1}{3})$

143. If $(1, 2), (-1, x)$ and $(2, 3)$ are collinear, then the value of 'x' is

-3

144. If the opposite vertices of a square are $(5, -4)$ and $(-3, 2)$ then the length of its diagonal is __units.

145. The distance between the points $(a cos \theta + b sin \theta, 0)$ and $(0, a sin \theta - b cos \theta)$ is

$a + b$

$\sqrt{a + b}$

$\sqrt{ a^{2} + b^{2} }$

$\sqrt{ a^{2} - b^{2} }$

146. The value of 'k' if the distance between $(k, 3)$ and $(2, 3)$ is 5 is

$\frac{3}{2}$

147. If $OPQR$ is a rectangle, where ‘O’ is the origin and $P(3, 0), R(0, 4)$ are two vertices, then the coordinates of 'Q' are

(3, 4)

(1, 3)

(3, -2)

(4, 3)

148. If $A(0, -1), B(2, 1)$ and $C(0, 3)$ are the vertices of $\bigtriangleup ABC$ , then the length of the median through 'B' is

149. If $A(4, y), B(6, 9)$ and $C(x, 4)$ are the vertices of $\bigtriangleup ABC$ and $(3, 6)$ is its centroid then $x - y$ =

-3

-2

-6

150. The coordinates of the midpoint of the line segment joining $(-8, 13)$ and $(x, 7)$ is $(4, 10)$ , then the value of $x^{2} - 5x + 1$ is

163

168

177

197

151. If the co-ordinates P, Q are $(a cos \theta, b sin \theta)$ and $(-a sin \theta, b cos \theta)$ and O is origin, then $OP^{2} + OQ^{2}$ =

$a + b$

$a^{2} + b^{2}$

$\sqrt{ a^{2} + b^{2} }$

$\sqrt{ a^{2} - b^{2} }$

152. If a vertex of a parallelogram is $(2, 3)$ and the diagonals cut at $(3, -2)$ , then the opposite vertex to $(2, 3)$ is

(4 , -7)

(2 , -5)

(1 , -2)

(-2 , -8)

153. If the points $(a, 0), (0, b)$ and $(1, 1)$ are collinear then

$a + b =0$

$\frac{1}{a} + \frac{1}{b} = 1$

$a + b = -1$

$\frac{1}{a} + \frac{1}{b} = 0$

154. The slope of a line perpendicular to $13x - 7y +1 = 0$ is

$-\frac{7}{13}$

-13

$-\frac{1}{13}$

155. The perimeter of triangle formed by the points $(0, 0), (1, 0)$ and $(0, 1)$ is __ units

$\sqrt{2}$

$(1 + \sqrt{2})$

$(2 + \sqrt{2})$

$\sqrt{3}$

156. If $P = (x, 2); Q = (8, 6)$ and $PQ^{2} = 25$ , then the value of 'x' is

5 or 11

1 or -3

-5 or $-\frac{1}{2}$

None

157. If the midpoints of the sides of ∆ABC are $(3, -1), (2, 6)$ and $(-5, 7)$ respectively, then area of $\bigtriangleup ABC$ is ___ sq.units

192

158. If $P(a, b), Q(a + 3, b + 4), R(a - 1, b + 7)$ are three vertices of a parallelogram $PQRS$ , then the coordinates of ‘S’ are

(a – 1, b + 2)

(a – 4, b + 3)

(a, b)

(-a, -b)

159. If $P(2, 1), Q(4, 2), R(5, 4)$ and $S(2, 3)$ are the vertices of a quadrilateral $PQRS$ , area of $PQRS$ is ___ sq.units

160. The height of equilateral triangle formed by $(-1, 0), (0, \sqrt{3})$ and $(1, 0)$ is __ units.

$\sqrt{2}$

$\sqrt{5}$

$\sqrt{3}$

$3\sqrt{3}$

161. If $A = (-\frac{8}{5}, 2)$ and $B = (\frac{2}{5}, 2)$ then $AB$ = __ units

$\sqrt{2}$

162. The triangle formed by $(\sqrt{3}-1,\sqrt{3}+1), (\sqrt{3}, 1)$ and $(\sqrt{3} + 1, \sqrt{3} + 1)$ is

Scalene triangle

Equilateral triangle

Isosceles triangle

Right triangle

163. If the line $\frac{x}{3} + \frac{y}{b} = 1$ passes through $(1, -1)$ then 'b' =

$-\frac{1}{2}$

$-\frac{3}{2}$

$-\frac{2}{3}$

$-\frac{1}{5}$

164. If $4x - 2y + 7 = 0$ and $y + ax = 8$ are parallel, then 'a' =

-2

165. Slope of a line which makes an angle of $\frac{3 \pi }{4}$ with the positive direction of x-axis is

-2

-1

166. One end of a diameter of a circle is $(2, 3)$ and the centre is $(-2, 5)$ , then the co-ordinates of the other end is

(-6, 7)

(1, -6)

(-2, 3)

(0, -6)

167. The coordinates of the centroid of the triangle with vertices $(0, 0), (3a, 0)$ and $(0, 3b)$ are

$(-a , -b)$

$(a , b)$

$(\frac{a}{2} , \frac{b}{2})$

$(\sqrt{a} , \sqrt{b})$

168. If the midpoint of the line segment joining $A( \frac{x}{2} , \frac{y + 1}{2})$ and $B(x + 1, y - 3)$ is $C(5, -2)$ then the values of 'x' and 'y' respectively are

1 , -3

0 , -1

5 , 3

6 , -1

169. If the point $P(x, y)$ is equidistant from $A(5, 1)$ and $B(-1, 5)$ then $3x - 2y$ =

-1

170. If the point $P(x, y)$ is equidistant from the points $A(a + b, b - a)$ and $B(a - b, a + b)$ then

$bx = ay$

$ax = by$

$a = b$

$b^{2} x = a^{2} y$

171. If $(3, 2)$ and $(-3, 2)$ are two vertices of an equilateral triangle which contains the origin, the third vertex is

$(1 , \sqrt{3})$

$(1 , 2 + \sqrt{3})$

$(0 , 2 + 3\sqrt{3})$

$(\sqrt{2} , \sqrt{3})$

172. If $(3, a)$ lies on the line $2x - 3y - 5 = 0$ , then 'a' =

-3

$\frac{1}{3}$

$\frac{1}{2}$

173. If $A(5, -1), B(-3, -2), C(-1, 8)[latex] are the vertices of [latex]\bigtriangleup ABC[latex], then the length of the median through 'A' is ___ units.</div><input type='hidden' name='question_id[]' id='qID_173' value='50949' /><input type='hidden' id='answerType50949' value='radio'></div><div class='question-choices watupro-choices-columns '><div class='watupro-question-choice ' dir='auto' ><input type='radio' name='answer-50949[]' id='answer-id-214784' class='answer answerof-50949 ' value='214784' /><label for='answer-id-214784' id='answer-label-214784' class=' answer'><span>4</span></label></div><div class='watupro-question-choice ' dir='auto' ><input type='radio' name='answer-50949[]' id='answer-id-214785' class='answer answerof-50949 ' value='214785' /><label for='answer-id-214785' id='answer-label-214785' class=' answer'><span>6</span></label></div><div class='watupro-question-choice ' dir='auto' ><input type='radio' name='answer-50949[]' id='answer-id-214786' class='answer answerof-50949 ' value='214786' /><label for='answer-id-214786' id='answer-label-214786' class=' answer'><span>14</span></label></div><div class='watupro-question-choice ' dir='auto' ><input type='radio' name='answer-50949[]' id='answer-id-214787' class='answer answerof-50949 ' value='214787' /><label for='answer-id-214787' id='answer-label-214787' class=' answer'><span>8</span></label></div></div></div></div><div class='watu-question ' id='question-174'><div id='questionWrap-174' class=' watupro-question-id-50952'> <div class='question-content' ><div><span class='watupro_num'>174. </span>The point on y - axis which is equidistant from [latex]A(6, 5)$ and $B(-4, 3)$ is

(1, 3)

(-1, -3)

(0, 9)

(0, 3)

175. If the points $A(-2, 1), B(a, b)$ and $C(4, 1)$ are collinear and $a - b = 1$ then $a + b$ =

-2

176. The ratio in which $(11, 15)$ divides the line segment joining the points $(15, 5)$ and $(9, 20)$ is

2 : 1

1 : 3

2 : 3

1 : 5

177. The value of 'p' if $(p + 1, 2p - 2), (p - 1, p)$ and $(p - 3, 2p - 6)$ are collinear is

-1

178. The area of quadrilateral $ABCD$ with vertices $A(5, -2), B(-3, -1), C(2, 1)$ and $D(6, 0)$ is ___ sq.units

179. The triangle formed by the points $(-2, 3), (8, 3)$ and $(6, 7)$ is

Scalene triangle

Right triangle

Equilateral triangle

None

180. The line segment joining the points $A(3, 2)$ and $B(5, 1)$ is divided at the point P in the ratio $1 : 2$ and P lies on the line $3x - 18y + k = 0$ , then the value of 'k' is

$\frac{8}{5}$

181. If $A(4, -1), B(5, 3), C(2, y)$ and $D(1, 1)$ are the vertices of a parallelogram, then 'y' =

-1

182. The triangle formed with $(3, -1), (5, -1)$ and $(3, -3)$ is

Scalene triangle

Equilateral triangle

Right angled scalene triangle

Isosceles right triangle

183. If $(a, b)$ is the midpoint of the segment joining the points $A(10, -6)$ and $B(k, 4)$ and $a - 2b = 18$ , then the distance between 'A' and 'B' is ___ units

$\sqrt{61}$

$2\sqrt{61}$

$\sqrt{31}$

$3\sqrt{31}$

184. If $R(x, y)$ is a point on the line segment joining the points $P(a, b)$ and $Q(b, a)$ then $x + y$ =

$a - b$

$b - a$

$a^{2}+ b -1$

$a + b$

185. The value of 'm' for which the point $P(m, 6)$ divides the line segment joining the points $A(-4, 3)$ and $B(2, 8)$ internally in the ratio $3 : 2$ is

$-\frac{1}{3}$

$-\frac{2}{3}$

$\frac{2}{5}$

$-\frac{2}{5}$

186. The area of the rhombus of vertices $(3, 0), (4, 5), (-1, 4)$ and $(-2, -1)$ taken in order is __ sq.units

187. The ratio in which the line joining the points $(a + b, b + a)$ and $(a - b, b - a)$ is divided by $(a, b)$ is

1 : 1

1 : 2

2 : 3

1 : 5

188. The area of $\bigtriangleup PQR$ formed by joining the midpoints of the sides of the triangle whose vertices are $A(1, -2), B(3, 2)$ and $C(-1, 4)$ is __ sq.units.

$5$

$\frac{5}{2}$

$\frac{5}{3}$

$\frac{1}{2}$

189. The value of 'x' for which the area of the triangle formed by $(5, -1), (x, 4)$ and $(6, 3)$ is 5.5 sq.m is

$\frac{5}{2}$

$\frac{7}{2}$

190. The area of a triangle is 5 sq.units. Two of its vertices are $(2, 1)$ and $(3, -2)$ . The third vertex lies on $y - x + 3 = 0$ . Then third vertex of that triangle is

(1, 3)

(-1, -3)

(0, -1)

(0, -3)

191. If the points $A(-2, k), B(3, -4)$ and $C(7, 10)$ are the vertices of a right angled isosceles triangle, the value of 'k' for $\angle A = 90^{0}$ is