Question

the only rule that will flip the order of x and y is 270° or 90° 270° or 180° 90° or 180°

Explanation:

In coordinate - geometry, a 90 - degree rotation counter - clockwise about the origin transforms a point (x, y) to (-y, x) and a 270 - degree rotation counter - clockwise about the origin transforms a point (x, y) to (y, -x), both of which flip the order of x and y coordinates. A 180 - degree rotation about the origin transforms (x, y) to (-x, -y) which does not flip the order of x and y in the sense of interchanging their positions.

Answer:

270° or 90°