COORDINATE GEOMETRY Test

COORDINATE GEOMETRY

This is COORDINATE GEOMETRY Test-04 for CBSE class 10 Maths.. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
Three consecutive vertices of a parallelogram ABCD are A(1, 2), B(1, 0) and C(4, 0). The co – ordinates of the fourth vertex D are
  • A
    (4, 2)
    Correct
  • B
    ( – 4, 2)
  • C
    (4, – 2)
  • D
    ( – 4, – 2)
2
The length of the median through A of \(\) \(\Delta ABC\) with vertices A(7, – 3), B(5, 3) and C(3, – 1) is
  • A
    5 units
    Correct
  • B
    3 units
  • C
    25 units
  • D
    7 units
3
If the line segment joining the points A\(({x_1},{y_1})\) and B\(({x_2},{y_2})\) is divided by a point P in the ratio 1 : k internally, then the co – ordinates of the point P are
  • A
    \(\left( {\frac{{{x_2} - k{x_1}}}{{1 + k}},\frac{{{y_2} - k{y_1}}}{{1 + k}}} \right)\)
  • B
    \(\left( {\frac{{{x_1} + k{x_2}}}{{1 + k}},\frac{{{y_1} + k{y_2}}}{{1 + k}}} \right)\)
  • C
    \(\left( {\frac{{{x_2} + k{x_1}}}{{1 + k}},\frac{{{y_2} + k{y_1}}}{{1 + k}}} \right)\)
    Correct
  • D
    \(\left( {\frac{{{x_2} + k{x_1}}}{{1 - k}},\frac{{{y_2} + k{y_1}}}{{1 - k}}} \right)\)
4
The base of an equilateral triangle ABC lies on the y – axis. The co – ordinates of the point C is (0, – 3). If origin is the midpoint of BC, then the co – ordinates of B are
  • A
    (0, 3)
    Correct
  • B
    ( – 3, 0)
  • C
    (0, – 3)
  • D
    (3, 0)
5
The point where the perpendicular bisector of the line segment joining the points A(2, 5) and B(4, 7) cuts is:
  • A
    (6, 3)
  • B
    (3, 6)
    Correct
  • C
    (0, 0)
  • D
    (2, 5)
6
If the point P(2, 1) lies on the line segment joining points A(4, 2) and B(8, 4), then
  • A
    \(AP = \frac{1}{4}AB\)
  • B
    \(AP = \frac{1}{2}AB\)
    Correct
  • C
    AP = PB
  • D
    \(AP = \frac{1}{3}AB\)
7
The centroid of a triangle divides the median in the ratio
  • A
    3 : 1
  • B
    none of these
  • C
    2 : 1
    Correct
  • D
    1 : 3
8
If the mid – point of the line segment joining the points (a, b – 2) and ( – 2, 4) is (2, – 3), then the values of ‘a’ and ‘b’ are
  • A
    6, – 8
    Correct
  • B
    6, 8
  • C
    4, – 5
  • D
    – 6, 8
9
If the points (2, 3), (4, k) and (6, – 3) are collinear, then the value of ‘k’ is
  • A
    1
  • B
    3
  • C
    4
  • D
    0
    Correct
10
If the points (x, y), (1, 2) and (7, 0) are collinear, then the relation between ‘x’ and ‘y’ is given by
  • A
    3x + y + 7 = 0
  • B
    x + 3y – 7 = 0
    Correct
  • C
    x – 3y + 7 = 0
  • D
    3x – y – 7 = 0
11
If the vertices of a triangle are (1, 1), ( – 2, 7) and (3, – 3), then its area is
  • A
    12 sq. units
  • B
    2 sq. units
  • C
    24 sq. units
  • D
    0 sq. units
    Correct
12
The area of the triangle with vertices (a, b+c), (b, c+a) and (c, a+b) is
  • A
    \({a^2} + {\text{ }}{b^2} + {\text{ }}{c^2}\)
  • B
    \({\left( {a{\text{ }} + {\text{ }}b{\text{ }} + {\text{ }}c} \right)^2}\)
  • C
    a + b + c
  • D
    0
    Correct
13
If points (a, 0), (0, b) and (1, 1) are collinear, then \(\frac{1}{a} + \frac{1}{b}\) is
  • A
    1
    Correct
  • B
    0
  • C
    – 1
  • D
    none of these
14
The area of the triangle formed by the vertices \(({x_1},{y_1})\), \(({x_2},{y_2})\) and \(({x_3},{y_3})\) is given by
  • A
    \(\frac{1}{2}\left[ {{x_1}({y_2} - {y_3}) + {x_2}({y_3} - {y_1}) + {x_3}({y_1} - {y_2})} \right]sq.units\)
    Correct
  • B
    \(\frac{1}{2}\left[ {{x_1}({y_2} - {y_3}) - {x_2}({y_3} - {y_1}) - {x_3}({y_1} - {y_2})} \right]sq.units\)
  • C
    \(\frac{1}{2}\left[ {{x_1}({y_2} + {y_3}) + {x_2}({y_3} + {y_1}) + {x_3}({y_1} + {y_2})} \right]sq.units\)
  • D
    \(\frac{1}{2}\left[ {{x_1}({y_2} + {y_3}) - {x_2}({y_3} + {y_1}) - {x_3}({y_1} + {y_2})} \right]sq.units\)
15
Three given points will be collinear, if the area of the triangle formed by these points is
  • A
    1 sq. units
  • B
    2 sq. units
  • C
    – 1 sq. units
  • D
    0 sq. units
    Correct