Thank you for reporting, we will resolve it shortly
Q.
Let $A(2, -3)$ and $B (-2, 1)$ be two angular points of $\Delta ABC$. If the centroid of the triangle moves on the line $2x + 3y = 1$, then the locus of the angular point $C$ is given by
Let the coordinates of $C$ be $(\alpha, \beta)$.
$\therefore $ Coordinates of centroid
$=\left(\frac{2-2+\alpha}{3}, \frac{-3+1+\beta}{3}\right)$
$=\left(\frac{\alpha}{3}, \frac{\beta-2}{3}\right)$
Since, centroid lie on $2 x+3 y=1$
$\therefore \frac{2 \alpha}{3}+3\left(\frac{\beta-2}{3}\right)=1 $
$\Rightarrow \frac{2 \alpha}{3}+\frac{3 \beta-6}{3}=1 $
$\Rightarrow 2 \alpha+3 \beta-6=3 $
$\Rightarrow 2 \alpha+3 \beta=9$
$\therefore $ Locus of point $C$ will be $2 x+3 y=9$