The line represented by the equation y=4-2x is the perpendi : GMAT Problem Solving (PS)
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# The line represented by the equation y=4-2x is the perpendi

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Manager
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The line represented by the equation y=4-2x is the perpendi [#permalink]

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03 Dec 2009, 07:23
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77% (02:06) correct 23% (00:50) wrong based on 132 sessions

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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)

OPEN DISCUSSION OF THIS QUESTION IS HERE: the-line-represented-by-the-equation-y-4-2x-is-the-127770.html
[Reveal] Spoiler: OA
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03 Dec 2009, 07:38
i solved the Q then I saw the figure you attached

is it (0,-1)?
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Manager
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03 Dec 2009, 07:52
lol.. i shd't have attached the figure then!
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03 Dec 2009, 08:53
even then its easy

For example :"Each diagonal of a square is the perpendicular bisector of the other. That is, each cuts the other into two equal parts, and they cross at right angles (90°)."

hence the (m1)(m2)=(-)1

math-polygons-87336.html
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22 Jun 2013, 11:48
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slope of the equation y = -2x + 4

slope of rp = 1/2

let p be (x,y)

then equation 1--- (y-1)/(x-4) = 1/2

also mid point lies on y = -2x + 4

so equation 2 -----(y+1)/2 = -2(x+4)/2 + 4

solve for both equations
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Re: The line represented by the equation y=4-2x is the perpendi [#permalink]

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22 Jun 2013, 11:59
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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)

There is no need of equations to solve this question. Plot the line y = 4 – 2x (just find the x and y intercepts and draw the line through them):

Now, it's easy to SEE that no blue point can be the mirror reflection of R around the line but (0, -1).

Similar question to practice:
in-the-rectangular-coordinate-system-above-the-line-y-x-144774.html
in-the-xy-coordinate-plane-is-point-r-equidistant-from-143502.html
in-the-rectangular-coordinate-system-the-line-y-x-is-the-132646.html
in-the-rectangular-coordinate-system-the-line-y-x-is-the-88473.html
in-the-rectangular-coordinate-system-above-the-line-y-x-129932.html

OPEN DISCUSSION OF THIS QUESTION IS HERE: the-line-represented-by-the-equation-y-4-2x-is-the-127770.html
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Re: The line represented by the equation y=4-2x is the perpendi   [#permalink] 22 Jun 2013, 11:59
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