Question

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

Answer 1

Let PQ be the perpendicular bisector of line segment AB.

Coordinates of $\theta =(\frac{6+2}{2},\frac{3-5}{2})$

$=(4,-1)$

Slope of AB$=\frac{y_2-y_1}{x_2-x_1}=\frac{-5-3}{6-2}$

$=-2$

Slope of $PQ=\frac{-1}{SlopeofAB}$

Slope of PQ$=\frac{1}{2}=m$

Equation of PQ$=y-y_1=m(x-x_1)$

$=y-3=\frac{1}{2}(x-2)$

$2y-6=x-2$

$\Rightarrow 2y-x=4$.