Coordinates of Point D in Square

This topic has expert replies
User avatar
Master | Next Rank: 500 Posts
Posts: 113
Joined: Sun Nov 24, 2013 9:19 pm
Thanked: 1 times
Followed by:5 members

Coordinates of Point D in Square

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
Attachments
Karishma_Quant2.png
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
GMAT Score:800

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]
Image

User avatar
Legendary Member
Posts: 1556
Joined: Tue Aug 14, 2012 11:18 pm
Thanked: 448 times
Followed by:34 members
GMAT Score:650

by theCodeToGMAT » Sun May 25, 2014 10:56 pm
{E}
Attachments
solution.jpg
R A H U L

User avatar
Master | Next Rank: 500 Posts
Posts: 113
Joined: Sun Nov 24, 2013 9:19 pm
Thanked: 1 times
Followed by:5 members

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.