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# The line represented by the equation y = 4 - 2x is the perpendicular bisector of line segment RP

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The line represented by the equation y = 4 - 2x is the perpendicular bisector of line segment RP. If R has the coordinates (4, 1), what are the coordinates of point P?

(A) (-4,1)

(B) (-2,2)

(C) (0,1)

(D) (0,-1)

(E) (2,0)

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the first step would be to figure out the slope of PR.  because y=4-2x is its perpendicular bisecor, then we know the slope of PR must be 1/2, thus y=1/2x+b
We can also figure out b by plugging in the point R (4,1)
1=1/2(4)+b thereforre b=-1
The final step is to figure out where P is.  Because we know that y=4-2x is the bisecor we know the section of the line from R to where it meets y=4-2x (let's call that A)  is equal to the part from A to P
to find where y=4-2x meets y=1/2(x)-1, we can set the equations equal to each other
4-2x=1/2(x)-1-----> x= 2 therefore y=0
We can then think of AR as right triangle with one vertice at (2,0) and one at (4,1), so one leg is 1 and the other is 2
thus the triangle created from AP should be the same, but the other way, over two and down one,  This is D.
If you want to double check, you can make sure that (0,-1) fits into y=1/2(x)-1
Hope this helps!

Eliza, GMAT Tutor

answered Jan 19, 2015 by Associate (125 points)
selected Feb 9, 2015 by
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Jyotsna Mehta