This exercise outlines a proof of the fact that two nonvertical lines with slopes m1 and...

This exercise outlines a proof of the fact that two nonvertical lines with slopes m₁ and m₂ are perpendicular if and only if m₁m₂= -1. In the following figure, we’ve assumed that our two nonvertical lines y = m₁x and y = m₂x intersect at the origin. [If they did not intersect there, we could just as well work with lines parallel to these that do intersect at (0, 0), recalling that parallel lines have the same slope.] The proof relies on the following geometric fact: