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Coordinates of Point D in Square

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by bml1105 » Sun May 25, 2014 4:06 pm
A square is drawn on the xy coordinate plane as shown (picture attached):

Its center lies at (0, 0). If it is rotated clockwise by 45° around the center point, what will be the (x, y) coordinates of point D?

(A) (−2,0)
(B) (2,2)
(C) (−2,2)
(D) (−2√,−2√)
(E) (−2√,2√)

OA: E
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Source: — Problem Solving |

by [email protected] » Sun May 25, 2014 5:18 pm
Hi bml1105,

This question can actually be solved with no math at all, but you will need to understand the logic behind the prompt.

Since the square is centered around the Origin, Point D is at (-2,0). IF we rotated the square 90 degrees clockwise, it would be where Point is now (0,2). But the question asks us to rotate it just 45 degrees clockwise, so Point D will land in the 2nd Quadrant (and have a NEGATIVE X -coordinate and have a POSITIVE Y-coordinate). Eliminate A, B and D.

In addition, rotating the square a full 360 degrees will send Point D through a complete CIRCLE, so you could do a rough sketch of what that would look like. You'll see that answer C would fall outside of that circle, so it can't be the answer. Eliminate C.

Final Answer: E

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
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by theCodeToGMAT » Sun May 25, 2014 10:56 pm
{E}
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by bml1105 » Mon May 26, 2014 7:19 pm
Thanks Rich! I think I fell for the trap answer of C because I wasn't thinking about the logic behind it.
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