Straight Lines and Pair of Straight Lines Part 1

Let the centroid of ΔPQR is (h, k) & P is(α, β), then

α+1+3

3

= h and

β+4−2

3

= k
α = (3h - 4) , β = (3k - 4)
Point P(α, β) lies on line 2x – 3y + 4 = 0
∴ 2(3h – 4) – 3(3k – 2) + 4 = 0
⇒ locus is 6x – 9y + 2 = 0