SOLUTION: A (5,2) is in the standard (x,y) coordinate place. what must be the coordinates of the point of B so that the line x=4 is the perpendicular bisector is AB? and why?
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Question 608872: A (5,2) is in the standard (x,y) coordinate place. what must be the coordinates of the point of B so that the line x=4 is the perpendicular bisector is AB? and why?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
In order for AB to be perpendicular to 
, a vertical line, the segment AB must be contained in a horizontal line. Horizontal lines have the characteristic that the 
coordinate of all points in the line are equal. Hence, if point A has a coordinate of 2, then point B must have a coordinate of 2 also. In order for to be the perpendicular bisector of AB, the point where intersects the line containing the segment AB must be the midpoint of AB. We know the 
coordinate of that midpoint because we know that 
, and we also know the coordinate of that midpoint because all points on the segement AB (indeed, all points on the line containing the segment AB) have a coordinate of 2. The distance from the point )
to the point )
can be calculated using the distance formula, or you can simply note that there is zero difference in the coordinates so the distance is the difference between the coordinates, i.e. 1. That means that point B has to be 1 unit on the other side of the midpoint, that is to say at )
John
My calculator said it, I believe it, that settles it
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