$\mathrm{A}=(2,5),\mathrm{B}=(4,-11)$ and the locus of C is $9\mathrm{x}+7\mathrm{y}+4=0.$ Then locus of the centroid of $\Delta \mathrm{ABC}$ is

$C (x,y)$ 
Centroid of $\Delta ABC=(h,k)$  
$(\frac{2+4+x}{3},\frac{5-11+y}{3})=h,k$ 
$\begin{array}{l}\frac{6+x}{3}=h\frac{-6+y}{3}=k\\ 6+x=3h-6+y+3k\\ x=3h-6y=3k+6\end{array}$ 
$9(3h+6)+7(3k+6)+4=0$ 
$27h+21k+102=0$ 
$reqlocusis27x+21y-8=0$