#### Answer

$ \frac{a-c}{e-c} =-1 $

#### Work Step by Step

For the two lines to be perpendicular, slopes must be opposite reciprocals. We use the equation for slope:
$ m_1 =\frac{b-d}{a-c}$
$ m_2 = \frac{b-d}{e-c}$
The reciprocal of $m_1$ times $m_2$ must equal -1. Thus, we find the equation:
$\frac{a-c}{b-d}\frac{b-d}{e-c} = -1 \\ \frac{a-c}{e-c} =-1 $