Question

in exercises 9 - 12, describe the rotation as (a) a counterclockwise rotation and (b) a clockwise rotation. then write a rule for the rotation.

Explanation:

Step1: Recall rotation rules

For a 90 - degree counter - clockwise rotation about the origin, the rule is $(x,y)\to(-y,x)$. For a 180 - degree counter - clockwise rotation about the origin, the rule is $(x,y)\to(-x,-y)$. For a 270 - degree counter - clockwise rotation about the origin (or 90 - degree clockwise rotation), the rule is $(x,y)\to(y, - x)$.

Step2: Analyze each figure

For each of the figures in Exercises 9 - 12, identify key points of the original shape (e.g., vertices of a polygon). Apply the appropriate rotation rule to each key point. Then connect the new points to form the rotated shape.
For example, if a point $A=(2,3)$ is rotated 90 - degree counter - clockwise about the origin, using the rule $(x,y)\to(-y,x)$, the new point $A'=(-3,2)$.

Answer:

Without specific exercise numbers and detailed instructions on which rotation to perform for each figure, a specific numerical answer cannot be provided. However, follow the above - mentioned rotation rules for each key point of the given shapes to find the rule for the rotation.