Question

answer a rotation 90° counterclockwise about the origin a translation 1 unit to the left and 9 units up a rotation 90° clockwise about the origin a translation 1 unit to the right and 9 units down

Explanation:

Step1: Recall rotation and translation rules

Rotation and translation are two types of transformations in geometry. For a $90^{\circ}$ counter - clockwise rotation about the origin, the transformation rule for a point $(x,y)$ is $(-y,x)$. For a $90^{\circ}$ clockwise rotation about the origin, the rule is $(y, - x)$. A translation $a$ units to the left and $b$ units up changes a point $(x,y)$ to $(x - a,y + b)$, and a translation $a$ units to the right and $b$ units down changes a point $(x,y)$ to $(x + a,y - b)$.

Step2: Analyze the transformation from Figure F to the other figure

By observing the orientation and position of the two figures, we can see that if we take a point on Figure F, say $(-5,-1)$, a $90^{\circ}$ counter - clockwise rotation about the origin would transform it to $(1,-5)$. If we consider the overall transformation of the figure, we can check the key points. A translation 1 unit to the left and 9 units up of a point $(x,y)$ gives $(x - 1,y + 9)$. A translation 1 unit to the right and 9 units down gives $(x + 1,y - 9)$. By comparing the orientation of the two figures, we find that a $90^{\circ}$ counter - clockwise rotation about the origin changes the orientation of Figure F to match the other figure.

Answer:

A rotation $90^{\circ}$ counterclockwise about the origin