A lot of reflections

Geometry Level 2

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 \(\frac{314}{379}.\)

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

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