COORDINATE GEOMETRY Test

COORDINATE GEOMETRY

This is COORDINATE GEOMETRY Test-03 for CBSE class 10 Maths.. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
The distance between the points (a, a) and \(( - \sqrt 3 a,\sqrt 3 a)\) is
  • A
    \(2\sqrt 2 {\text{ }}units\)
  • B
    \(2{\text{ }}units\)
  • C
    \(3\sqrt 2 a{\text{ }}units\)
  • D
    \(2\sqrt 2 a{\text{ }}units\)
    Correct
2
The distance between the points (sinθ, cosθ) and (cosθ, – sinθ) is
  • A
    \(\sqrt 2 {\text{ }}units\)
    Correct
  • B
    \(2\sqrt 2 {\text{ }}units\)
  • C
    \(2{\text{ }}units\)
  • D
    \(\sqrt {\sin \theta + \cos \theta } {\text{ }}units\)
3
The distance between the points \(A(p{\text{ }}sin{\text{ }}25^\circ ,{\text{ }}0)\) and \(B(0,{\text{ }}p{\text{ }}sin{\text{ }}65^\circ )\) is
  • A
    1 units
  • B
    0 units
  • C
    p units
    Correct
  • D
    \({p^2}units\)
4
The distance between \((a{t^2},2at)\) and \(\left( {\frac{a}{{{t^2}}},\frac{{ - 2a}}{t}} \right)\) is
  • A
    \(a\left( {{t^2} + \frac{1}{{{t^2}}}} \right){\text{ }}units\)
  • B
    \({\left( {t + \frac{1}{t}} \right)^{\text{2}}}{\text{ }}units\)
  • C
    \(a{\left( {t + \frac{1}{t}} \right)^{\text{2}}}{\text{ }}units\)
    Correct
  • D
    \(a{\left( {t - \frac{1}{t}} \right)^{\text{2}}}{\text{ }}units\)
5
The co – ordinates of the mid – point of the line segment joining the points \(({x_1},{y_1})\)and \(({x_2},{y_2})\) is given by
  • A
    \(\left( {\frac{{{x_1} - {x_2}}}{2},\frac{{{y_1} - {y_2}}}{2}} \right)\)
  • B
    \(\left( {\frac{{{x_1} - {y_1}}}{2},\frac{{{x_2} - {y_2}}}{2}} \right)\)
  • C
    \(\left( {\frac{{{x_1} + {x_2}}}{2},\frac{{{y_1} + {y_2}}}{2}} \right)\)
    Correct
  • D
    \(\left( {\frac{{{x_1} + {y_1}}}{2},\frac{{{x_2} + {y_2}}}{2}} \right)\)
6
The point where the medians of a triangle meet is called the ________ of the triangle
  • A
    centroid
    Correct
  • B
    none of these
  • C
    orthocentre
  • D
    circumcentre
7
The co – ordinates of the mid – point of the line segment joining the points ( – 2, 3) and (4, – 5) are
  • A
    (1, – 1)
    Correct
  • B
    ( – 1, 1)
  • C
    ( – 2, 4)
  • D
    (0, 0)
8
If the end points of a diameter of a circle are ( – 4, – 3) and (2, 7), then the co – ordinates of the centre are
  • A
    (2, – 1)
  • B
    ( – 1, 2)
    Correct
  • C
    (1, – 2)
  • D
    (0, 0)
9
If one end of a diameter of a circle is (2, 3) and the centre is ( – 2, 5), then the other end is
  • A
    (0, 8)
  • B
    (6, – 7)
  • C
    (0, 4)
  • D
    ( – 6, 7)
    Correct
10
The co – ordinates of the mid – point of the line joining the points (3p, 4) and ( – 2, 4) are (5, p). The value of ‘p’ is
  • A
    3
  • B
    1
  • C
    2
  • D
    4
    Correct
11
The co – ordinates of the point which divides the join of ( – 6, 10) and (3, – 8) in the ratio 2 : 7 is
  • A
    ( – 1, 3)
  • B
    ( – 4, 6)
    Correct
  • C
    (1, – 3)
  • D
    (4, – 6)
12
The ratio in which the point (1, 3) divides the line segment joining the points ( – 1, 7) and (4, – 3) is
  • A
    2 : 3
    Correct
  • B
    2 : 7
  • C
    3 : 2
  • D
    7: 2
13
The centroid of a triangle whose vertices are (3, – 7), ( – 8, 6) and (5, 10) is
  • A
    (3, 3)
  • B
    (0, 3)
    Correct
  • C
    (1, 3)
  • D
    (0, 9)
14
If the point M( – 1, 2) divides the line segment PQ in the ratio 3 : 4, where the co – ordinates of P are (2, 5), then the co – ordinates of Q are
  • A
    (5, – 2)
  • B
    ( – 5, – 2)
    Correct
  • C
    (5, 2)
  • D
    ( – 5, 2)
15
The centroid of a triangle whose vertices are \(({x_1},{y_1})\), \(({x_2},{y_2})\) and \(({x_3},{y_3})\) is given by
  • A
    \(\left( {\frac{{{x_1} + {x_2} + {x_3}}}{2},\frac{{{y_1} + {y_2} + {y_3}}}{2}} \right)\)
  • B
    \(\left( {\frac{{{x_1} + {x_2} + {x_3}}}{4},\frac{{{y_1} + {y_2} + {y_3}}}{4}} \right)\)
  • C
    \(\left( {\frac{{{x_1} + {x_2} + {x_3}}}{6},\frac{{{y_1} + {y_2} + {y_3}}}{6}} \right)\)
  • D
    \(\left( {\frac{{{x_1} + {x_2} + {x_3}}}{3},\frac{{{y_1} + {y_2} + {y_3}}}{3}} \right)\)
    Correct