Question

rotations as functions quick check
which of the following mappings is used for a 270 - degree (counterclockwise) rotation? (1 point)
○ (x,y)→(−y,−x)
○ (x,y)→(−y,x)
○ (x,y)→(−x,−y)
○ (x,y)→(y,−x)

Explanation:

Step1: Recall rotation rules

In a 2 - D coordinate system, for a 270 - degree counter - clockwise rotation, we can use the general rotation matrix or memorize the transformation rule. The rule for a 270 - degree counter - clockwise rotation of a point $(x,y)$ about the origin is based on the relationship between the original and new coordinates.

Step2: Identify the correct mapping

The mapping for a 270 - degree counter - clockwise rotation of a point $(x,y)$ is $(x,y)\to(y, - x)$.

Answer:

$(x,y)\to(y, - x)$