The transformation \((x, y) \to (y, -x)\) represents a 270-degree counterclockwise rotation because it swaps the coordinates and negates the new x-coordinate, effectively moving points counterclockwise around the origin. In this rotation, the original x-coordinate becomes the new y-coordinate, and the original y-coordinate is inverted, resulting in the correct placement of the point after the specified rotation angle.
explain why (x,y)→(y,−x) is used for a 270-degree (counterclockwise) rotation? (answer in 2 sentences )
1 answer