Question

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

Answer 1

The right bisector of a line segment bisects the line segment at ${90}^{\circ }$

The end-points of the line segment are given as $A(3,4)$ and $B(-1,2)$

Accordingly, mid-point of $AB=(\frac{3-1}{2},\frac{4+2}{0})=(1,3)$

Slope of $AB=\frac{2-4}{-1-3}=\frac{-2}{-4}=\frac{1}{2}$

$\therefore$ Slope of the line perpendicular to $AB=-\frac{1}{\left(\frac{1}{2}\right)}=-2$

The equation of the line passing through $(1,3)$ and having a slope of $-2$ is

$(y-3)=-2(x-1)$

$Y-3=-2x+2$

$2x+y=5$

Thus, the required equation of the line is $2x+y=5$.