AMC 10B 2025 (Problem 25)

Square

ABCD

has sides of length

4

. Points

P

and

Q

lie on

\overline{AD}

and

\overline{CD}

, respectively, with

AP=\frac{8}{5}

and

DQ=\frac{10}{3}

. A path begins along the segment from

P

Q

and continues by reflecting against the sides of

ABCD

(with congruent incoming and outgoing angles). If the path hits a vertex of the square, it terminates there; otherwise it continues forever. At which vertex does the path terminate?

\text{(A)}\;\text{A}

\text{(B)}\;\text{B}

\text{(C)}\;\text{C}

\text{(D)}\;\text{D}

\text{(E)}\;\text{The path continues forever.}