2025 AMC 10B Problem 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?

\textbf{(A)} A \qquad \textbf{(B)} B \qquad \textbf{(C)} C \qquad \textbf{(D)} D \qquad \textbf{(E)} The path continues forever.

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.