Question

Find the equation of the perpendicular bisector of the straight line segment joining the points $(3,4),(-1,2)$.

Answer 1

Let $A(3,4),B(-1,2)$ be given points $CD$ be required perpendicular bisector.
$C$ is the mid point of $AB$
Coordinate of $C=(\frac{3-1}{2},\frac{4+2}{2})=(1,3)$
Slope of $AB=\frac{y_2-y_1}{x_2-x_1}$
$=\frac{2-4}{-1-3}$

$=\frac{-2}{-4}=\frac{1}{2}$
$CD\perp AB$
Slope of $CD=-2$
The equation of $CD$ is
$y-y_1=m(x-x_1)$
$\Rightarrow y-3=-2(x-1)$
$\Rightarrow y-3=-2x+2$
$\Rightarrow 2x+y-3-2=0$
$\Rightarrow 2x+y-5=0$