In this section we state that two lines, neither of which is vertical, are perpendicular if and only if their slopes have a product of -1. we outline a partial proof of this for the case where the two lines intersect at the origin.

By the converse of the Pythagorean theorem, if

then triangle POQ is a right triangle with right angle at O.

Find an expression for the distance d(O, P).

y 2%3D 2 1%3 ( *) (x, ) [d(0, P)]? + [d(0, Q)] = [d(P, Q)],