Question

rotations as functions quick check
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

In a 2 - D coordinate system, for a counter - clockwise rotation of 270 degrees about the origin, we can use the general rotation matrix or memorize the transformation rule.

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 rotation matrix \(

$$\begin{bmatrix}0&1\\- 1&0\end{bmatrix}$$

$$\begin{bmatrix}x\\y\end{bmatrix}$$

=

$$\begin{bmatrix}y\\-x\end{bmatrix}$$

\).

Answer:

\((x,y)\to(y, - x)\) (the second option)