Straight Lines and Pair of Straight Lines Part 1

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) + A,(3x - y + 1) = 0
∵ It passes through (2, 2)
⇒7+5λ=0⇒λ=−

7

5

∴ Required line is 8 x - 11 y + 6 = 0
∵ (-9, -6) satisfies this equation.