Question

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

Explanation:

Step1: Recall rotation rules

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

Step2: Analyze the orientation of the figures

By observing the orientation of Figure I and Figure J, we can see that Figure J is obtained from Figure I by a 90 - degree counter - clockwise rotation about the origin. If it were a 90 - degree clockwise rotation, the orientation would be different. A 180 - degree rotation would flip the figure in a different way. And the translation would not change the orientation but just the position without rotating the figure.

Answer:

A rotation 90° counterclockwise about the origin