First we are going to find the slope of these two endpoints.
Slope = [tex] \frac{Y2-Y1}{X2-X1} [/tex]
Slope = [tex] \frac{9-1}{-9-7} [/tex]
Slope = [tex] \frac{8}{-16} [/tex]
Slope = [tex]- \frac{1}{2} [/tex]
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 = [tex]( \frac{X1+X2}{2} , \frac{Y1+Y2}{2} )[/tex]
Mdpt = [tex]( \frac{7+(-9)}{2} , \frac{1+9}{2} )[/tex]
Mdpt = [tex]( \frac{-2}{2} , \frac{10}{2} )[/tex]
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
