The equation of perpendicular bisector of the line segment joining $\mathrm{A}(-2,3)$ and $\mathrm{B}(6,-5)$…
The equation of perpendicular bisector of the line segment joining $\mathrm{A}(-2,3)$ and $\mathrm{B}(6,-5)$ is
$x+y=3$
$x+y=1$
$x-y=-1$
$x-y=3$
Solution
Slope of line $\mathrm{AB}=\frac{-5-3}{6+2}=\frac{-8}{3}=-1$
Mid point of $\mathrm{AB}=\frac{-2+6}{2}, \frac{3-5}{2}=(2,-1)$
Equation of perpendicular bisector $\mathrm{AB}$ is $(\mathrm{y}+1)=1(\mathrm{x}-2)$ i.e. $x-y=3$