Question

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:

1. Recall transformation rules:

• For a 180 - degree clock - wise rotation about the origin, the rule is \((x,y)\to(-x,-y)\).
• For a 90 - degree clock - wise rotation about the origin, the rule is \((x,y)\to(y, - x)\).
• For a 90 - degree counter - clockwise rotation about the origin, the rule is \((x,y)\to(-y,x)\).
• For a translation 2 units to the right and 2 units up, the rule is \((x,y)\to(x + 2,y + 2)\). Without the original and transformed figures, we can analyze the general nature of these transformations. Each rotation changes the orientation of a figure around the origin, and the translation just moves the figure without changing its orientation.

Answer:

No answer can be determined without the original and transformed figures shown in the graph.