Question

The equation of the perpendicular bisector of the line segment joining $A(-2,3)$ and $B(6,-5)$ is

• A. $x-y=-1$
• B. $x-y=3$
• C. $x+y=3$
• D. $x+y=1$
• E. $x+y=-1$

Answer 1

Answer: (B)

The equation of the line passing through the points $(-2,3)$ and $(6,-5)$ is $(y-3)=\frac{-5-3}{6+2}(x+2)$
$\Rightarrow$ $(y-3)=-1(x+2)$
$\Rightarrow$ $y-3=-x-2$
$\Rightarrow$ $y=-x+1$ ..(i)
Now, the slope of perpendicular bisector of this line is
$=\frac{-1}{(-1)}=1$ and the perpendicular bisector passing through the mid point of this line is $(2,-1)$ . Then, equation of perpendicular bisector is $(y+1)=1(x+2)$
$\Rightarrow$ $y+1=x-2$
$\Rightarrow$ $x-y=3$