Question

describe the rotation as a (a) counterclockwise rotation and (b) clockwise rotation.
write a rule for the rotation.
$(x,y)\to(\square,\square)$

Explanation:

Step1: Observe the transformation

By looking at the pre - image $\triangle ABC$ and the image $\triangle A'B'C'$, we can determine the angle of rotation.

Step2: Determine counter - clockwise rotation

Count the number of 90 - degree turns from the pre - image to the image. We see that $\triangle ABC$ is rotated 270 degrees counterclockwise about the origin to get $\triangle A'B'C'$.

Step3: Determine clockwise rotation

Since a full rotation is 360 degrees, a 270 - degree counterclockwise rotation is equivalent to a 90 - degree clockwise rotation.

Step4: Find the rotation rule

The rule for a 270 - degree counterclockwise (or 90 - degree clockwise) rotation about the origin is $(x,y)\to(y, - x)$.

Answer:

a. 270°
b. 90°
$(x,y)\to(y, - x)$