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. None of these

Answer 1

Answer: (C)

$6x+4y=1$

Let $A(1,2)$ and $(-2,0)$

Mid point of $\overline{AB}=(\frac{1-2}{2},\frac{2+0}{2})=(-1/2,1)$

Slope of $\overline{AB}-\frac{0-2}{-2+(-1)}=\frac{-2}{-3}=\frac{2}{3}$

Slope of perpendicular bisector $=-\frac{3}{2}$

$\therefore$ equation of perpendicular bisectore:

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

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

or, $4y-4=-6x-3$

or, $6x+4y=1$