Question

Find the equation of perpendicular bisector of line segment joining the points $(-3,4)$ and $(7,-8)$

Answer 1

Equation of line joining the given points:

$\frac{y-4}{x+3}=\frac{-12}{10}=-6/5$

$5y-20=-6x-18$

$5y+6x-2=0$

slope = -6/5

Slope of perpendicular line: -5/6

Midpoint: $\left(\right(7-3)/2,(4-8\left)/2\right)=(2,-2)$

Line we need: $y=\frac{-5}{6}x+c$

this passes through (2,-2) implies:

-2=-5/3+c

c=5/3-2=-1/3Required Line" $y=\frac{-5}{6}x-1/3$

$6y+5x+2=0$