Question 139382: Point A(-4,1) is in the standard (x,y) coordinate plane. What must be the coordinares of point B so that the line x=2 is the perpendicular bisector of line AB.
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website! The line  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 . That means the point of intersection between 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 and the segment is just the absolute value of the difference in the x-coordinates of Point A and the point of intersection, namely  .
In order for 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 
In summary, Point B is (8,1)
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