The distance between the two points ( 2, 3 ) and ( 1, 4 ) is ______.

(a)

2

(b)

\(\sqrt { 56 } \)

(c)

\(\sqrt { 10 } \)

(d)

\(\sqrt { 2 } \)

If the points A (2, 0), B (-6, 0), C (3, a-3) lie on the x-axis then the value of a is _____.

(a)

0

(b)

2

(c)

3

(d)

-6

If the coordinates of one end of a diameter of a circle is (3, 4) and the coordinates of its centre is (−3, 2), then the coordinate of the other end of the diameter is ______.

(a)

(0, −3)

(b)

(0, 9)

(c)

(3, 0)

(d)

(−9, 0)

The ratio in which the x-axis divides the line segment joining the points A(a₁, b₁) and B(a₂, b₂ ) is ______.

(a)

b₁ : b₂

(b)

−b₁ : b₂

(c)

a₁ : a₂

(d)

−a₁ : a₂

The ratio in which the x-axis divides the line segment joining the points (6, 4) and (1, −7) is ______.

(a)

2:3

(b)

3:4

(c)

4:7

(d)

4:3

If the coordinates of the mid-points of the sides AB, BC and CA of a triangle are (3, 4), (1, 1) and (2, −3) respectively, then the vertices A and B of the triangle are ______.

(a)

(3, 2), (2, 4)

(b)

(4, 0), (2, 8)

(c)

(3, 4), (2, 0)

(d)

(4, 3), (2, 4)

The mid-point of the line joining (−a, 2b) and (−3a,−4b) is ______.

(a)

(2a, 3b)

(b)

(−2a, −b)

(c)

(2a, b)

(d)

(−2a, −3b)

In what ratio does the y-axis divides the line joining the points (−5, 1) and (2, 3) internally ______.

(a)

1 :3

(b)

2 :5

(c)

3 :1

(d)

5 :2

If (1,−2), (3, 6), (x, 10) and (3, 2) are the vertices of the parallelogram taken in order, then the value of x is ______.

(a)

6

(b)

5

(c)

4

(d)

3

The centroid of the triangle with vertices (−1, −6), (−2, 12) and (9, 3) is

(a)

(3, 2)

(b)

(2, 3)

(c)

(4, 3)

(d)

(3, 4)