Question

answer a rotation 90° counterclockwise about the origin a translation 2 units to the right and 2 units up a rotation 180° counterclockwise about the origin a rotation 90° clockwise about the origin

Explanation:

Step1: Recall rotation rules

For a 90 - degree counter - clockwise rotation about the origin, the transformation rule for a point $(x,y)$ is $(-y,x)$. For a 180 - degree counter - clockwise rotation about the origin, the rule is $(-x,-y)$. For a 90 - degree clockwise rotation about the origin, the rule is $(y, - x)$. For a translation 2 units to the right and 2 units up, the rule is $(x + 2,y+2)$.

Step2: Analyze the transformation from Figure B to Figure C

By observing the orientation and position of the figures, we can see that if we take a point $(x,y)$ on Figure B and transform it to Figure C, it follows the rule of a 90 - degree counter - clockwise rotation about the origin. For example, if we consider a vertex of Figure B at $(2,0)$ and its corresponding vertex on Figure C at $(0,2)$.

Answer:

A. A rotation 90° counterclockwise about the origin