Question 25
Square $ABCD$ has sides of length $4.$ Points $P$ and $Q$ lie on $\overline{AD}$ and $\overline{CD},$ respectively, with $AP = \tfrac{8}{5}$ and $DQ = \tfrac{10}{3}.$ A path begins along the line segment from $P$ to $Q$ and continues by reflecting against the sides of $ABCD$ (with congruent incoming and outgoing angles), as shown in the figure. If the path hits a vertex of the square, then it terminates there; otherwise it continues forever.
At which vertex does the path terminate?
At which vertex does the path terminate?