# 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?

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?
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Matthew Benton
Let,the coordinate of B is (a,b)
So,if AB 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 AB 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 (8,1)