Question

Let C be the centroid of the triangle with vertices (3, –1), (1, 3) and (2, 4). Let P be the point of intersection of the lines x + 3y – 1 = 0 and 3x – y + 1 = 0. Then the line passing through the points C and P also passes through the point : 

(1) (7, 6)

(2) (–9, –6)

(3) (–9, –7)

(4) (9, 7)

Answer 1

Answer is (2) (–9, –6)

Centroid of Δ = (2, 2)

line passing through intersection of

x + 3y - 1 = 0 and

3x - y + 1 = 0, be given by

(x + 3y - 1) + λ(3x - y + 1) = 0

If passes through (2, 2)

⇒ 7 + 5λ = 0 ⇒ λ = - 7/5

∴ Required line is 8x - 11y + 6 = 0

∵ (-9, - 6) satisfies this equation.

Answer 2

Answer is (2) (-9, - 6)