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Challenge 380: Line Location

Where is the mirror in this laser beam set-up?

 A laser is positioned at the point (1, 1) on the x-y plane.

A flat mirror is placed at right angles to the plane standing on top of a straight line L, and the laser beam is reflected by this mirror.

The beam hits the mirror at the point (4, -3) and also passes through through the point (-20, 15).

Find the equation of L.