Question

Let $A(6,4)$ and $B(2,12)$ be two given points, then the equation of perpendicular bisector of $AB$ is

• A. $x+2y-12=0$
• B. $x-2y-12=0$
• C. $x+2y+12=0$
• D. $x-2y+12=0$

Answer 1

The correct option is D $x-2y+12=0$

Perpendicular bisector will pass through mid point of $AB$
Hence the coordinate of the midpoint of $AB$ is
$(4,8)$
Now slope of perpendicular bisector $=-\frac{1}{\text{slope of}AB}=-\frac{6-2}{4-12}=\frac{1}{2}$
Hence the required equation is
$y-8=\frac{1}{2}(x-4)\Rightarrow x-2y+12=0$