SOLUTION: Please help me with this 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

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Question 256075: Please help me with this
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?
Found 3 solutions by richwmiller, solver91311, stanbon:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
x=2 is a vertical line going through (2,y)
A perpendicular line would be horizontal going through (2,y) and from the point (-4,1) we know the y value is 1 so the point C intersection of the lines is (2,1)
An equation for that line could be y=1 (There are an infinite number of such lines)
2-(-4)=6
2+6=8
since x=2 bisects the line AB
point B should be (8,1)

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


is a vertical line. Therefore the line containing the segment AB must be a horizontal line. All points in any horizontal line have identical coordinates. Therefore, since the -coordinate of A(-4,1) is 1, the -coordinate of point B must also be 1.

The -coordinate of all points in any given vertical line are identical. Therefore, the -coordinate of all points on the line is 2. That means that the midpoint of the segment AB must be (2,1).

The midpoint formula for gives the -coordinate of the midpoint given the -coordinates of the endpoints:



But here we know the -coordinate of one of the endpoints and the -coordinate of the midpoint. So solve the formula for



Substitute the known values and do the arithmetic.



Therefore B is the point (8, 1)

John

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
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?
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Draw the picture so you can see what you are doing.
Plot the point: (-4,1)
Draw the line x=2; it will pass thru (2,1) and (2,1) will be the mid-point
of AB.
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Let the coordinates of B be (x,y):
(-4+x)/2 = 2
-4+x = 4
x = 8
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(1+y)/2 = 1
1+y = 2
y = 1
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The coordinate of B are (8,1)
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Cheers,
Stan H.