Place an isosceles right triangle with its right angle at the origin and legs along the positive x- and y-axes.

Imagine this triangle is three mirrors and a laser is fired from the origin with some positive slope.

The laser will bounce around and one of 3 possibilities will occur:
1. The laser will eventually come back to the origin.
2. The laser will eventually hit one of the other corners.
3. The laser will never hit any of the corners.

For a given slope, how can you tell which will happen?