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Cant form the equation

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by [email protected] » Tue Aug 06, 2013 6:36 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)
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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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