A point P moves on the line 2x-3y+4=0.

Question

A point $P$ moves on the line $2x-3y+4=0$. If $Q(1,4)$ and $R(3,-2)$ are fixed points, then the locus of the centroid of $	riangle PQR$ is a line:

Accepted Answer

Let the centroid of $$\Delta $$PQR is (h, k) \& P is ($$\alpha $$, $$\beta $$),  then

$${{\alpha  + 1 + 3} \over 3} = h\,$$   and   $${{\beta  + 4 - 2} \over 3} = k$$

$$\alpha  = \left( {3h - 4} \right)$$   $$\beta  = \left( {3k - 4} \right)$$

Point P($$\alpha $$, $$\beta $$) lies on the line 2x - 3y + 4 = 0

$$ \therefore $$  2(3h - 4) - 3 (3k - 2) + 4 = 0

$$ \Rightarrow $$  locus  is 6x - 9y + 2 = 0

Solutions · 1