Question 205592
First, AB with a line above it is shorthand for "line segment AB".
Given point A is (-4, 1).
Now since the line segment AB is bisected by the perpendicular line x = 2, (a vertical line) then you can conclude that the midpoint of line segment AB is at the point (2, 1).
Why, because the line segment AB is horizontal and we know this because the line x = 2 (a vertical line) is the perpendicular bisector of line segment AB, and the line x = 2 must pass through the center of the line segment AB and intersect it at the point (2, 1).
So, using the midpoint formula which gives us the x- and y-coordinates of the midpoint (2, 1):
{{{((x[1]+x[2])/2)}}},{{{((y[1]+y[2])/2)}}} where: {{{x[1] = -4}}} and {{{y[1] = 1}}} substituting, we get:
{{{((-4+x[2])/2) = 2}}} and...
{{{((1+y[2])/2) = 1}}} we can solve for {{{x[2]}}} and {{{y[2]}}} which will be the x- and y-coordinates of point B.
{{{(-4+x[2])/2 = 2}}} Multiply both sides by 2.
{{{-4+x[2] = 4}}} Now add 4 to both sides.
{{{highlight(x[2] = 8)}}} and for the y-coordinate of B...
{{{(1+y[2])/2 = 1}}} Multiply both sides by 2.
{{{1+y[2] = 2}}} Subtract 1 from both sides.
{{{highlight(y[2] = 1)}}} 
The coordinates of point B are (8, 1)