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…
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
$2 x+3 y=9$
$2 x-3 y=7$
$3 x+2 y=5$
$3 x-2 y=3$
Solution
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 $2 x+3 y=9$