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 y comma negative x right parenthesis (x,y)→(−y,−x) left parenthesis x comma y right parenthesis right arrow left parenthesis negative y comma negative x right parenthesis (x,y)→(−y,x)

Answer 1

To determine the correct mapping for a 270-degree counterclockwise rotation, we can analyze how each point (x, y) transforms under this rotation.

A 270-degree counterclockwise rotation is equivalent to a 90-degree clockwise rotation. The transformation for a 90-degree clockwise rotation can be represented as follows: \[ (x, y) \rightarrow (y, -x) \] So, for a 270-degree counterclockwise rotation, we need to find the correct mapping among the given options:

1. (x,y)→(−x,−y): This represents a rotation of 180 degrees, not 270 degrees.
2. (x,y)→(y,−x): This represents a 90-degree clockwise rotation (or a 270-degree counterclockwise rotation), so this is the correct mapping.
3. (x,y)→(−y,−x): This too represents a 180-degree rotation, not 270 degrees.
4. (x,y)→(−y,x): This represents a 90-degree counterclockwise rotation.

The correct answer to the question is: (x,y)→(y,−x) (which corresponds to the 270-degree counterclockwise rotation).