rotating 90 degrees around a circle on a co-ordinate plane !enter image description here I thought the answer would be square root of 3. It would seem that the x co-ordinate of Q would just be the opposite of the x co-ordinate of P. I'm not sure if the picture is just being deceptive, or if I just don't remember my math from high school very well... However... I'm told the correct answer is 1. I don't understand why... Could someone explain that please? Thanks so much!

A simple answer to your question is that when you rotate by $90$ degrees (as indicated by the right angle symbol), you swap the $x$ and $y$ coordinates and then negate one or the other, depending on which direction you rotated it. In your case, you had $(-\sqrt{3}, 1)$, which became $(1, -\sqrt{3})$ and then because you rotated into the first quadrant, the final point is $(1, \sqrt{3})$.