SOLUTION: point A (-4,1) is in the standard (x,y) coordintae 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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The line is a vertical line thru the point (2,0).
You are asked to find point B such that the line x=2, is both perpendicular to and bisecting the line segment AB
Since is vertical (an undefined slope), then the segment AB must be horiztonal. In order to horizontal, the y coordinate from B must be the same as the y coordinate in point A.
so B =
The x coordinate of A is -4, so that coordinate is 2 - (-4) = 6 units from the nearest point on the line
In order to be bisector, that means the closest point to B is also a distance of 6.
so B = =
Now plot them and see if the logic works :)