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by GMATGuruNY » Tue Aug 06, 2013 7:25 pm
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)

OA:D
Just draw a picture of what is being described. A perpendicular bisector:

-- intersects at the midpoint
-- forms a right angle

Here's my rudimentary drawing:

Image

Looking at the drawing above, we can see that P must have a negative y-coordinate.
Only answer choice D works.

The correct answer is D.

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by macattack » Tue Aug 06, 2013 11:51 pm
For those who are not into drawing here is how I approach such problems:
The perpendicular bisector bisects the line RP at its midpoint. Call the point I. Now choosing P we need to make sure that I's coordinate verify the equation of the bisector since it is the intersection point.
x(i)=(x(p)+x(r))/2 y(i)=(y(p)+y(r))/2
Plug in the different answer choice into the above equation get the coordinate of i and then plug them into the equation of the bisector and see if they verify that equation!
Only answer D does the job.
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by Uva@90 » Sat Aug 10, 2013 10:12 pm
[email protected] wrote: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)
shibsriz,
An another method,
As we know that when two lines are perpendicular then product of the slope of two lines is -1
So from the given statement, y=4-2x,the slop of the line is -2.
So, -2*m = -1 => m = 1/2

We know the one point of the second line i.e. (4,1)
So (y2-y1)/(x2-x1)=m => (y2-1)/(x2-4) = 1/2 Substitute options given.
The only option that matches is [spoiler]D(0,-1)[/spoiler]

Regards,
Uva
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