Question

Let $A(2,-3)$ and $B(-2,1)$ be vertices of a triangle of a $ABC$. If the centroid of this triangle moves on the line $2x+3y=1$, then the locus of the vertices $C$ is the line

• A. $3x-2y=6$
• B. $2x-3y=7$
• C. $3x+2y=5$
• D. $2x+3y=9$

Answer 1

The correct option is D $2x+3y=9$

Let the third vertex be $C(h,k)$
$\therefore$ Centroid of $\Delta ABC$ is
$G(\frac{2-2+h}{3},\frac{-3+1+k}{3})\equiv G(\frac{h}{3},\frac{k-2}{3})$
Which lies on $2x+3y=1$
$\therefore \frac{2h}{3}+3\left(\frac{k-2}{3}\right)=1$
$⟹2h+3k=9$