help math

Write an equation of the perpendicular bisector of the segment with endpoints M(1,5) and N(7,−1).

Hello Guest!

The center of the given segment is \(P\ (\frac{7+1}{2},\frac{-1+5}{2})\) so \(P\ (4,2)\)

\(m=-\frac{x_2-x_1}{y_2-y_1}=-\frac{7-1}{-1-5} \)

\(m=1\)

Point-direction equation \(f(x)=m(x-x_P)+y_P\)

\(f(x)=1(x-4)+2\)

The equation of the perpendicular bisector of the segment with endpoints M(1,5) and N(7,−1) is \(f(x)=x-2\)

  !