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by gmatapril » Sat Feb 26, 2011 3:34 pm
194. In the rectangular coordinate system above, the line
y = x is the perpendicular bisector of segment AB (not
shown), and the x-axis is the perpendicular bisector of
segment BC (not shown). If the coordinates of point A
are (2,3), what are the coordinates of point C ?
(A) (-3,-2)
(B) (-3,2)
(C) (2,-3)
(D) (3,-2)
(E) (2,3)
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by Night reader » Sat Feb 26, 2011 4:01 pm
think for a second :) the line y=x can bisect line segment AB only if the angle in the point of bisection is 90`. So this will make another side equal to Srt(13) which can be easily found from A (2;3) - but forget this now; we need another line to be equal to A-O origin line segment - this could be B (2;3) for having angle in the point of bisection =90`. The question further suggests that BC is also bisected by abscess x. It's only possible when the same line segment portion lies below y=0 or C (3;-2) and answer D.
gmatapril wrote:194. In the rectangular coordinate system above, the line
y = x is the perpendicular bisector of segment AB (not
shown), and the x-axis is the perpendicular bisector of
segment BC (not shown). If the coordinates of point A
are (2,3), what are the coordinates of point C ?
(A) (-3,-2)
(B) (-3,2)
(C) (2,-3)
(D) (3,-2)
(E) (2,3)
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by GMATGuruNY » Sat Feb 26, 2011 4:17 pm
gmatapril wrote:194. In the rectangular coordinate system above, the line
y = x is the perpendicular bisector of segment AB (not
shown), and the x-axis is the perpendicular bisector of
segment BC (not shown). If the coordinates of point A
are (2,3), what are the coordinates of point C ?
(A) (-3,-2)
(B) (-3,2)
(C) (2,-3)
(D) (3,-2)
(E) (2,3)
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 point C must have a positive x coordinate and a negative y coordinate.
Eliminate A, B and E.
Since point C is more to the right than is point A, the x coordinate of point C must be greater than 2.
Eliminate C.

The correct answer is D.
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by gmatapril » Mon Feb 28, 2011 12:52 pm
your explanations are always great and shortcut
GMATGuruNY wrote:
gmatapril wrote:194. In the rectangular coordinate system above, the line
y = x is the perpendicular bisector of segment AB (not
shown), and the x-axis is the perpendicular bisector of
segment BC (not shown). If the coordinates of point A
are (2,3), what are the coordinates of point C ?
(A) (-3,-2)
(B) (-3,2)
(C) (2,-3)
(D) (3,-2)
(E) (2,3)
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 point C must have a positive x coordinate and a negative y coordinate.
Eliminate A, B and E.
Since point C is more to the right than is point A, the x coordinate of point C must be greater than 2.
Eliminate C.

The correct answer is D.
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