Question

Find the equation of perpendicular bisector of the line segment joining the points $A(2,3)$ and $B(6,-5)$.

Answer 1

Since, the slope of the line $AB$

$=\frac{y_2-y_1}{x_2-x_1}$

$=\frac{-5-3}{6-2}$

$=\frac{-8}{4}=-2$

But slope of perpendicular bisector will be

$=-\frac{1}{m}=\frac{1}{2}$

Therefore, the equation of the line

$y+1=\frac{1}{2}(x-4)$

$2y+2=x-4$

$x-2y=6$

Hence, this is the answer.