Question

Find the equation of the $\perp$ bisectors of the line segment joining the points $A(2,3)$ and $B(6,-5)$ ?

Answer 1

$A(2,3)$ and $B(6,-5)$

mid-point of $A,B=(4,-1)$

$\perp$ bisector is $\perp$ to line through $AB$ and passes through the mid point of $AB$.

$\therefore$ slope of line through $AB=\frac{8}{-4}=-2$

$\therefore$ slope of line $\perp$ to $AB=\frac{1}{2}$

$\therefore$ Equation of $\perp$ bisector $(y+1)=\frac{1}{2}(x-4)$

$\Rightarrow x-2y-6=0$