How would you do it without a computer or program?

If you do not understand rotation in radians, tackle this problem in a way that you understand. There are multiple ways to determine which area the mouse is in.

How would you do it on graph paper?

If the mouse is above the middle or below the middle would give you the upper half or lower half... Now you have cut out one possible option, either the top or bottom.

If the mouse is to the left of center or right of center... Now you cut out either the left or right side leaving only two possible options.

The only thing left to do is determine which side of the diagonal line the mouse is in, because in all possible cases you are left with a square 1/4 the original size cut in half corner to corner