Question

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

Answer 1

Given,

$(1,3),(3,1)$

mid point $=(\frac{1+3}{2},\frac{3+1}{2})=(2,2)$

slope $=\frac{1-3}{3-1}=-1$

Therefore slope of perpendicular bisector $=1$

Equation of line passing through $(2,2)$ having slope $1$ is,

$(y-2)=1(x-2)$

$\therefore x-y=0$