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).
\(m=\frac{4}{3},x_1=3,y_1=-2
\\y-y_1=m(x-x_1)
\\
\\y-(-2)=\frac{4}{3}(x-3)
\\
\\y+2=\frac{4}{3}x-\frac{8}{3}
\\
\\3y+6=4x-8
\\4x-3y-14=0\)