Question

In a triangle ABC, coordinates of A are (1, 2) and the equations of the medians through B and C are x + y = 5 and x = 4 respectively. Then coordinates of B and C will be

(a) (– 2, 7), (4, 3)

(b) (7, – 2), (4, 3)

(c) (2, 7), (– 4, 3)

(d) (2, – 7), (3, – 4)

Answer 1

The correct option (b) (7, – 2), (4, 3)

Explanation:

A(1, 2), B(x1, y1) & c(x2, y2)

equation of median through B is x1 + y1 = 5

equation of median through C is x2 = 4

∴ solving we get x = 4 & y = 1

∴ G = (4, 1)

∴ 4 = [(1 + x1 + x2)/3] & 1 = [(y1 + y2 + 2)/3]

∴ x1 + x2 = 11 & y1 + y2 = 1

∴ x1 = 11 – 4 = 7 and y2 = 1 + 2 = 3

∴ (x1, y1) = (7, – 2) and (x2, y2) = (4, 3)