Coordinate Geometry: JEE Main 2025 Mathematics question

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