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# 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 the 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¯ ?

-4 is 6 units from 2 on the x-axis
now go 6 units to the right from 2 on the x-axis to get to 8(you said bisect-divide into two equal pieces)
the y coordinate is 1 again because the lines are perpendicular
(8,1) is the point

The line x = 2 is a vertical line.  Since this vertical line is to be the perpendicular bisector of the line joining A and B, the line joining A and B must be a horizontal line.  This means that the y coordinate of point B must be the same as that of point A -  that is 1.   The remaining issue is to find the x coordinate of point B.  Since -4 (the x coordinate of point A) is to the left of  the line x =2,   the x coordinate of point B must be to the right of the line x = 2.   We want the point (2, 1) to be the mid point of the line joining A and B.   The coordinates of B which do that are (8, 1).    The value 2 is the average of 8 and -4, and   points A, B and the intersection of the two lines all have the same y value - that is 1.

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