Question

The equation of perpendicular bisector of the line segment joining the points $(1,2)$ and $(-2,0)$ is

• A. $5x+2y=1$
• B. $4x+6y=1$
• C. $6x+4y=1$
• D. $noneofthese$

Answer 1

Answer: (C)

$6x+4y=1$

$A(1,2)$ and $B(-2,0)$ are given point

$\therefore$ midpoint $p=(\frac{1+(-2)}{2},\frac{2+0}{2})$

$\therefore$ midpoint $p=(\frac{-1}{2},1)$

Also slope of $AB=\frac{0-\left(2\right)}{-2-1}=\frac{-2}{-3}$

$\therefore$ slope of $AB=\frac{2}{3}$

slope of line perpendicular to $AB=\frac{-1}{\frac{2}{3}}=\frac{-3}{2}$

$\therefore$ equation of perpendicular bisector

$y-1=\frac{-3}{2}(x+\frac{1}{2})$

$\therefore y-1=\frac{-3}{2}(x+\frac{1}{2})$

$\therefore 2y-2=-3(x+\frac{1}{2})$

$\therefore 4y-4=-3(2x+1)$

$\therefore 4y-4=-6x-3$

$\therefore 4y+6x-4+3=0$

$6x+4y-1=0$

$\therefore$ equation of line $6x+4y-1=0$