Question

If the coordinates of $A$ and $B$ be $(1,1)$ and $(5,7)$, then the equation of the perpendicular bisectors the line segment $AB$ is

• A. $2x+3y=18$
• B. $2x-3y+18=0$
• C. $2x+3y-1=0$
• D. $3x+2y+1=0$

Answer 1

The correct option is A $2x+3y=18$

Slope of line $AB=\frac{7-1}{5-1}=\frac{3}{2}$

Slope of perpendicuar bisector of $AB=\frac{-1}{\left(\frac{3}{2}\right)}=\frac{-2}{3}$

Mid-point of $AB=(\frac{5+1}{2},\frac{7+1}{2})=(3,4)$

Therefore, Equation of perpendicular bisector of $AB$-

$y-4=\frac{-2}{3}(x-3)$

$3(y-4)=-2(x-3)$

$3y-12=-2x+6$

$2x+3y-12-6$

$2x+3y-18=0$

$\Rightarrow 2x+3y=18$