Question

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

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

Answer 1

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

Let coordinates of $C$ be $(h,k).$
Then, centroid of $△ABC$ is $(\frac{2-2+h}{3},\frac{-3+1+k}{3})=(\frac{h}{3},\frac{k-2}{3})$
Given, centroid lies on the line $2x+3y=1$
$\therefore \frac{2h}{3}+3\left(\frac{k-2}{3}\right)=1$
$\Rightarrow 2h+3k=9$
Hence, locus of $C$ is $2x+3y=9$