Question

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

Explanation:

Step1: Recall rotation rules

For a 270 - degree counter - clockwise rotation about the origin, the general rule is based on the relationship between the original coordinates $(x,y)$ and the new coordinates.

Step2: Apply the rule

The mapping for a 270 - degree counter - clockwise rotation of a point $(x,y)$ about the origin is $(x,y)\to(y, - x)$. This can be derived from the properties of rotation in the coordinate plane.

Answer:

$(x,y)\to(y, - x)$ (the third option)