Let the triangle PQR be the image of the triangle with vertices (1,3), (3,1) and (2,4) in the line x+2 y=2. If the centroid of Δ PQR is the point (α,…

Let the triangle PQR be the image of the triangle with vertices $\displaystyle (1,3)$, $\displaystyle (3,1)$ and $\displaystyle (2,4)$ in the line $\displaystyle x+2 y=2$. If the centroid of $\displaystyle \Delta \mathrm{PQR}$ is the point $\displaystyle (\alpha, \beta)$, then $\displaystyle 15(\alpha-\beta)$ is equal to :