# Point A(-4,1) is in standard (x,y) coordinate plane. What must be the coordinates of point B so that the line x=2 is the perpendicular bisector of ab?

Mar 10, 2018

Let,the coordinate of $B$ is $\left(a , b\right)$

So,if $A B$ is perpendicular to $x = 2$ then,its equation will be $Y = b$ where $b$ is a constant as slope for the line $x = 2$ is ${90}^{\circ}$, hence the perpendicular line will have a slope of ${0}^{\circ}$

Now,midpoint of $A B$ will be $\left(\frac{- 4 + a}{2}\right) , \left(\frac{1 + b}{2}\right)$

clearly,this point will lie on $x = 2$

So, $\frac{- 4 + a}{2} = 2$

or, $a = 8$

And this will lie as well on $y = b$

so, $\frac{1 + b}{2} = b$

or, $b = 1$

So,the coordinate is $\left(8 , 1\right)$