Question

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

Answer 1

Midpoint of the points $(3,4)$ and $(-1,2)$

$=(\frac{3-1}{2},\frac{4+2}{2})=(1,3)$

Slope of a line joining points $(3,4)$ and $(-1,2)$ $=\frac{2-4}{-1-3}=\frac{1}{2}$

Slope of the required line = $-2$
[as they are perpendicular]

So, equation of required line is $(y-3)=(-2)(x-1)$

$\Rightarrow y-3=-2x+2$

$\Rightarrow 2x+y=5.$