The coordinates of A' after a 90-degree counterclockwise rotation around the origin are (2, 2), which corresponds to answer D) A'(2, 2).
When a point is rotated 90 degrees counterclockwise around the origin in Cartesian coordinates, the coordinates of the point change in a specific way. The original point's x-coordinate becomes the new y-coordinate, and the original y-coordinate becomes the negative of the new x-coordinate. To illustrate, if we have a point A with coordinates (x, y), the coordinates of A' after a 90-degree counterclockwise rotation will be (-y, x).
Applying this rule to the given point A(2, -2), the new coordinates for A' after a 90-degree counterclockwise rotation about the origin will be (-(-2), 2), which simplifies to (2, 2). Therefore, the correct answer is D) A'(2, 2).