Question

The equation of the perpendicular bisector of the line segment joining $(2,1)$ and $(3,4)$ is

• A. $x+3y-10=0$
• B. $x+3y+10=0$
• C. $x-3y-10=0$
• D. $x-y+10=0$

Answer 1

The correct option is A $x+3y-10=0$

Mid point of line segment joining $(2,1)$ and $(3,4)$ $\equiv (\frac{5}{2},\frac{5}{2})$
Slope of the line joining $(2,1)$ and $(3,4)$
$m=\frac{4-1}{3-2}=3$
The required line is perpendicular to it, hence slope of the line $=-\frac{1}{m}=-\frac{1}{3}$
Equation of perpendicular bisector : $y-\frac{5}{2}=-\frac{1}{3}(x-\frac{5}{2})$
$\Rightarrow 2y-5=\frac{-1}{3}(2x-5)\Rightarrow x+3y-10=0$