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The line represented by the equation y=4-2x is the perpendi

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The line represented by the equation y=4-2x is the perpendi [#permalink] New post 03 Dec 2009, 07:23
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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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Re: bisector [#permalink] New post 03 Dec 2009, 07:38
i solved the Q then I saw the figure you attached :lol:

is it (0,-1)?
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Re: bisector [#permalink] New post 03 Dec 2009, 07:52
lol.. i shd't have attached the figure then!
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Re: bisector [#permalink] New post 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
where m1,m2 are gradients

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Re: bisector [#permalink] New post 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] New post 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):
Image
Now, it's easy to SEE that no blue point can be the mirror reflection of R around the line but (0, -1).

Answer: D.

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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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