Triangle ABC has vertices A=(0, 1), B=(1, 0) and C=(0, 0) in the coordinate plane.

The insides of the sides are lined with mirrors, and then a laser beam is fired from the origin with a slope of 314/379

Which corner of the triangle will the laser beam hit first?

(In reply to

There are easy ways by Jer)

Agree. I do not know why Charlie is counting hypotenuses. It seems to me that you just reduce p and q to lowest terms.

Then:

If numerator and denominator are both odd, the answer is (0,0)

If numerator is even, the answer is (1,0)

If denominator is even, the answer is (0,1)

In the case of 314/379, this makes my answer (1,0). This has the advantage of agreeing with Charlie's answer.