JEE 2025 — Mathematics PYQ

$\therefore △PQR$ is image of $△ABC$ with respect to line  
$x+2y=2$

Centroid of $△ABC$

$G=\left(2,\frac{8}{3}\right)$

$\therefore$ Centroid of $△PQR$ is $G^{\prime }(\alpha ,\beta )$  

That is image of $G$ w.r.t. $x+2y-2=0$

Using image formula,

$\frac{\alpha -2}{1}=\frac{\beta -\frac{8}{3}}{2}<br>=-2\left(\frac{2+\frac{16}{3}-2}{1+4}\right)$

$\frac{\alpha -2}{1}=\frac{\beta -\frac{8}{3}}{2}<br>=-\frac{32}{15}$

$\alpha -2=-\frac{32}{15}$

$\alpha =2-\frac{32}{15}=-\frac{2}{15}$

$\beta -\frac{8}{3}=-\frac{64}{15}$

$\beta =\frac{8}{3}-\frac{64}{15}=-\frac{24}{15}$

$\therefore 15(\alpha -\beta )=22$