Question

figure f figure e answer a translation 4 units to the left and 4 units down a rotation 90° counterclockwise about the origin a rotation 180° clockwise about the origin a rotation 90° clockwise about the origin submit answer

Explanation:

Step1: Recall transformation rules

For a point $(x,y)$ rotated 90 - degree counter - clockwise about the origin, the new point is $(-y,x)$; for 90 - degree clockwise, it is $(y, - x)$; for 180 - degree clockwise or counter - clockwise, it is $(-x,-y)$; for a translation $a$ units left and $b$ units down, the new point $(x,y)$ becomes $(x - a,y - b)$.

Step2: Analyze the transformation from Figure E to Figure F

Let's take a vertex of Figure E, say $(4,1)$.
If we rotate it 90 - degree counter - clockwise about the origin, the new coordinates are $(-1,4)$.
If we rotate it 90 - degree clockwise about the origin, the new coordinates are $(1,-4)$.
If we rotate it 180 - degree clockwise about the origin, the new coordinates are $(-4,-1)$.
If we translate it 4 units to the left and 4 units down, the new coordinates are $(4 - 4,1 - 4)=(0,-3)$.
By observing the orientation and position of Figure E and Figure F, if we take a general point $(x,y)$ of Figure E and rotate it 90 - degree counter - clockwise about the origin, we get the corresponding point of Figure F.

Answer:

A rotation 90° counterclockwise about the origin