# How do I write an equation for the perpendicular bisector of the segment joining the points (5,-4) and (-3,-2)?

Jan 21, 2016

$y = 4 x - 7$

#### Explanation:

The slope of the line in which the two points lay is $k = {\Delta}_{y} / {\Delta}_{x}$. The slope of the line perpendicular to that one is $p = - \frac{1}{k} = - {\Delta}_{x} / {\Delta}_{y}$.
$p = - \frac{{x}_{2} - {x}_{1}}{{y}_{2} - {y}_{1}} = - \frac{5 + 3}{- 4 + 2} = \frac{8}{2} = 4$

The midpoint is $\left(1 , - 3\right)$

So the require equation is
$\left(y + 3\right) = 4 \left(x - 1\right)$
$y = 4 x - 4 - 3$
$y = 4 x - 7$