Question

Points $AandB$ have coordinates $(7,-3)and(1,9)$ respectively. Find the equation of the perpendicular bisector of the line segment $AB$.

Answer 1

middle point of AB $=(\frac{7+1}{2},\frac{-3+9}{2})$

$=(4,3)$

Also slope of AB $=\frac{(9-(-3\left)\right)}{1-7}=-2$

$\therefore \perp$ bisector of AB has slope $=\frac{-1}{-2}=\frac{1}{2}$

$\therefore$ Equation :-

$y-3=1/2(x-4)$

$\therefore 2y-6=x-4$

$\therefore 2y-x-2=0$