Hi Gmat_mission.
We can find the correct answer discarding the wrong answers.
First, because of the position of D after the rotation, we can conclude that before the rotation it was on the quadrant II. Therefore, the x-coordinate was negative and the y-coordinate was positive.
This allows us to discard the options A, B and D.
On the other hand, from the picture we can see that the distance from D to the origin must be 2 (it doesn't change after the rotation). Now, let's find the distance between C and O: $$d\left(C,O\right)=\sqrt{\left(-2-0\right)^2+\left(2-0\right)^2}=\sqrt{8}\ne2.$$ So, we discard C.
Hence, the correct answer is _E_. In additon,
$$d\left(E,O\right)=\sqrt{\left(-\sqrt{2}-0\right)^2+\left(\sqrt{2}-0\right)^2}=\sqrt{4}=2.$$
I hope it helps you.
Regards.
