Question

figure l answer a rotation 90° counterclockwise about the origin a rotation 180° counterclockwise about the origin a translation 8 units to the right and 4 units down a rotation 90° clockwise about the origin

Explanation:

Step1: Recall rotation rules

The rule for a 90 - degree counter - clockwise rotation about the origin is $(x,y)\to(-y,x)$. For a 180 - degree counter - clockwise rotation about the origin is $(x,y)\to(-x,-y)$ and for a 90 - degree clockwise rotation about the origin is $(x,y)\to(y, - x)$. A translation 8 units to the right and 4 units down has the rule $(x,y)\to(x + 8,y-4)$.

Step2: Analyze the figure transformation

By observing the orientation of the figure before and after transformation, we can see that the figure's orientation has changed in a way that is consistent with a 90 - degree counter - clockwise rotation about the origin. The shape's position and orientation match the result of applying the $(x,y)\to(-y,x)$ rule to each vertex of the original figure.

Answer:

A rotation 90° counterclockwise about the origin