Question

write an equation of the perpendicular bisector of the line segment whose endpoints are (-1,1) and (7,-5)

Answer 1

Find midpoint of segment.
(-1,1), (7,-5)
$x= \frac{-1+7}{2}=3,y= \frac{1+(-5)}{2}=-2$

Find slope of line which passes through (-1,1) and (7,-5).
$m= \frac{-5-1}{7-(-1)}= \frac{-6}{8}=- \frac{3}{4}$

The slope of perpendicular line is negative reciprocal value of m.
$m_{\perp}=- \frac{1}{m} =- \frac{1}{- \frac{3}{4} } = \frac{4}{3}$

Write quation of line which slope is $\frac{4}{3}$ and passes throug the point (3,-2).
$m=\frac{4}{3},x_1=3,y_1=-2 \\y-y_1=m(x-x_1) \\ \\y-(-2)=\frac{4}{3}(x-3) \\ \\y+2=\frac{4}{3}x-\frac{8}{3} \\ \\3y+6=4x-8 \\4x-3y-14=0$