Question

pentagon efghi is the image of pentagon efghi under a rotation 90° counterclockwise about the origin followed by a reflection. write the rules for the rotation and reflection. rotation: (x, y) → ( , ) reflection: (x, y) → ( , )

Explanation:

Step1: Recall rotation rule

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

Step2: Analyze reflection

By observing the positions of the pre - image and the final image, we can see that the reflection is over the y - axis. The rule for a reflection over the y - axis is $(x,y)\to(-x,y)$.

Answer:

Rotation: $(x,y)\to(-y,x)$
Reflection: $(x,y)\to(-x,y)$