Question

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

Explanation:

Step1: Recall rotation rules

In a 2 - D coordinate system, for a 270 - degree counter - clockwise rotation of a point $(x,y)$ about the origin, we can use the general rotation matrix or memorize the transformation rule.

Step2: Apply the rule

The rule 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 rotation matrix

$$\begin{bmatrix}0&1\\- 1&0\end{bmatrix}\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}y\\-x\end{bmatrix}$$

.

Answer:

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