Let $A = (0, 1)$ and $B = (2, 0)$ in the plane. Let $O$ be the origin and $C = (2, 1)$ . Consider $P$ moves on the segment $OB$ and $Q$ move on the segment $AC$.
Find the coordinates of $P$ and $Q$ for which the length of the path consisting of the segments $AP, PQ$ and Q$B$ is least.