Which of the following mappings is used for a 270-degree (counterclockwise) rotation?(1 point) Responses (x,y)→(−x,−y) left parenthesis x comma y right parenthesis right arrow left parenthesis negative x comma negative y right parenthesis (x,y)→(−y,x) left parenthesis x comma y right parenthesis right arrow left parenthesis negative y comma x right parenthesis (x,y)→(y,−x) left parenthesis x comma y right parenthesis right arrow left parenthesis y comma negative x right parenthesis (x,y)→(−y,−x)

Answer 1

For a 270-degree counterclockwise rotation of the point \((x, y)\) in the coordinate plane, the correct mapping is:

\[ (x,y) \rightarrow (y, -x) \]

This transformation reflects the new position of the point after a 270-degree rotation around the origin.

To summarize:

• A 90-degree counterclockwise rotation maps \((x, y)\) to \((-y, x)\).
• A 180-degree rotation maps \((x, y)\) to \((-x, -y)\).
• A 270-degree counterclockwise rotation (or 90 degrees clockwise) maps \((x, y)\) to \((y, -x)\).

Thus, the answer is:

\[ (x,y) \rightarrow (y, -x) \]