In this coordinate plane, line m is perpendicular to line n.

Complete the proof that the slope of m is equal to the opposite reciprocal of the slope of n.
Line m is perpendicular to line n, which means
is a right angle. So,
is a right triangle. The altitude
BD
to the hypotenuse in the right triangle △ACD creates two
right triangles, △ABD and △DBC. Since
,
AB
BD
=
BD
BC
. Further, since AB=a, BD=b, and BC=c,
by substitution.
The slope of a line is defined as the change in y divided by the change in x. Two points on line m are D(0,0) and A(b,a). So, the slope of line m is
. Two points on line n are D(0,0) and C(b,
–
c). So, the slope of line n is
. This means the opposite reciprocal of the slope of n is
. Therefore, the slope of m is equal to the opposite reciprocal of the slope of n.