A(2,3),B(3,-5) are two vertices of $∆$ABC. If the centroid of the $∆$ABC moves on the line 2x + y - 2 = 0, then the locus of C is

Let C = (x,y). Then centroid of $∆$A B C is $\mathrm{G}=\left(\frac{2+3+\mathrm{x}}{3},\frac{3-5+\mathrm{y}}{3}\right)=\left(\frac{\mathrm{x}+5}{3},\frac{\mathrm{y}-2}{3}\right)$
G lies on the line 2x +y -2 =0 $\Rightarrow 2\left(\frac{\mathrm{x}+5}{3}\right)+\left(\frac{\mathrm{y}-2}{3}\right)-2=0\Rightarrow 2\mathrm{x}+10+\mathrm{y}-2-6=0$
$\Rightarrow$2x + y +2=0