Question

Find the equation of the perpendicular bisector of the line segment joining points $(7,1)$ and $(3,5)$.

Answer 1

Since it is a perpendicular bisector, hence point M is the midpoint

$\therefore$ Midpoint $\left(AB\right)=[\frac{7+3}{2},\frac{5+1}{2}]=[\frac{10}{2},\frac{6}{2}]=M[5,3]$

Slope $\left(AB\right)m_1=\frac{3-7}{5-1}=\frac{-4}{4}=-1m_1\times m_2=-1-1\times m_2=-1m_2=1$

Equation of perpendicular bisector.
$=(y-3)=1(x-5)y-3=x-5x-y-2=0$