Bunuel
A square is drawn on the xy coordinate plane as shown:

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. \((−\sqrt{2},−\sqrt{2})\)
E. \((−\sqrt{2},\sqrt{2})\)
Attachment:
Karishma_Quant2.png
They key to solving this question is understanding what constitutes a 45 degree clockwise rotation and how that actually changes the position of point "D." More fundamentally, if we rotate the figure 45 degrees clockwise then the X coordinate for point D would be equal to negative half of the length of line AD. The trap in this question is essentially getting test takers to think that because point "O" is the origin, then the length of AD, BA, BC, DC as the figure resembles a rotated square. However, this is not actually the case. If we know the length of triangle AOD's hypotenuse then we calculate x and y coordinate of point. Moreover, this question also presents answer chances that can be quickly "eyeballed" and eliminated provided the test taker knows the properties of each quadrant of the graph ( example all x and y values in quadrant iii must be negative). Anyways, point O" is equidistant from point A and point D- therefore, the length of both AO and AD is 2. If we use the Pythagoren Theorem then we can solve for the length of side AD, the hypotenuse.
Length of Side AD (hypotenuse)2^2 + 2^2 = 8
\sqrt{8}=
(4)\sqrt{2}=
2\sqrt{2}
Now if we divide this length by two and convert it to negative, then we have the x value of "D"
-\sqrt{2}/2
According to the properties of Quadrant III (which we already know D must be in by definition of a 45 degree clockwise rotation), answer choices D, B and A clearly cannot be the coordinates of D. The only two choices are "C" and "E." Knowing that point D's x value must be -\sqrt{2} the answer must be E.
Hence "E"