Question 139382
The line {{{x=2}}} is a vertical line.  Therefore if it is to be the perpendicular to anything, that anything must be a horizontal line.  The important characteristic of any horizontal line is that every ordered pair comprising that line has an identical y-coordinate.  That means that if Point A and Point B are in the same horizontal line, their y-coordinates must be equal, and we can say immediately that the y-coordinate of Point B is 1.


The characteristic of vertical lines is that all of the x-coordinates are equal, and in this case equal to 2, because the equation of the line is {{{x=2}}}.  That means the point of intersection between {{{x=2}}} and the line segment AB must have an x-coordinate of 2.  Since the line segment AB is horizontal, the distance from Point A to the point of intersection between {{{x=2}}} and the segment is just the absolute value of the difference in the x-coordinates of Point A and the point of intersection, namely {{{abs(-4-2)=6}}}.


In order for {{{x=2}}} to be the bisector of the segment, the distance from B to the point of intersection must equal the distance from A to the point of intersection.  Note that the x-coordinate of A is negative, and the x-coordinate of the point of intersection is positive, so Point A is to the left of the point of intersection.  Therefore Point B must be to the right of the point of intersection, which is to say that the x-coordinate of B must be greater than the x-coordinate of the intersection.  We know that the amount it must be greater is 6 because that is the distance from A to the intersection, hence the x-coordinate of B is {{{2+6=8}}}


In summary, Point B is (8,1)