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Let $A(2,-3)$ and $B(-2,1)$ be vertices of a triangle $A B C$. If the centroid of this triangle moves on the line $2 x+3 y=1$, then the locus of the vertex $C$ is the line
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$2 x+3 y=9$
$2 x+3 y=9$
If $\mathrm{C}$ be $(\mathrm{h}, \mathrm{k})$ then centroid is $(\mathrm{h} / 3,(\mathrm{k}-2) / 3)$ it lies on $2 x+3 y=1$. $\Rightarrow$ locus is $2 x+3 y=9$
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