Olympiad Geometry · Superchallenge problem

Two parallel mirrors lie along the lines $y = 0$ and $y = 4$. A light ray starts at $A(0, 1)$, reflects once off the mirror $y = 4$, then once off the mirror $y = 0$, and then arrives at $B(12, 3)$. (At each mirror the angle of incidence equals the angle of reflection.) Find the total length of the light's path.