Question

Find an equation for the perpendicular bisector of the line segment whose endpoints are (7,1)(7,1) and (-9,9)(−9,9)

Answer 1

First we are going to find the slope of these two endpoints.

Slope = $\frac{Y2-Y1}{X2-X1}$

Slope = $\frac{9-1}{-9-7}$
Slope = $\frac{8}{-16}$
Slope = $- \frac{1}{2}$

Because we need the perpendicular bisector, we do the opposite reciprocal of the slope. This is positive two. 

Your perpendicular equation begins as y = 2x + b

To find where it will bisect, we need to find the midpoint of the two endpoints. 

Midpoint = $( \frac{X1+X2}{2} , \frac{Y1+Y2}{2} )$

Mdpt = $( \frac{7+(-9)}{2} , \frac{1+9}{2} )$
Mdpt = $( \frac{-2}{2} , \frac{10}{2} )$
Mdpt = (- 1, 5)

We plug this into our incomplete equation to solve for b.

5 = 2(- 1) + b
5 = - 2 + b
7 = b

Your perpendicular bisector equation is y = 2x + 7