Question

figure $defg$ is the image of figure $defg$ under a rigid motion. which rigid motions map figure $defg$ onto figure $defg$? select all that apply.
90 degree clockwise rotation around point $o$
90 degree counter - clockwise rotation around point $o$
180 degree rotation around point $o$
270 degree clockwise rotation around point $o$
270 degree counter - clockwise rotation around point $o$

Explanation:

Step1: Recall rotation rules

For a 90 - degree clockwise rotation of a point $(x,y)$ around the origin $(0,0)$, the new point is $(y, - x)$. For a 90 - degree counter - clockwise rotation, the new point is $(-y,x)$. For a 180 - degree rotation, the new point is $(-x,-y)$. For a 270 - degree clockwise rotation (same as 90 - degree counter - clockwise), the new point is $(-y,x)$ and for a 270 - degree counter - clockwise rotation (same as 90 - degree clockwise), the new point is $(y, - x)$.

Step2: Analyze the transformation

By observing the orientation of figure $DEFG$ and its image $D'E'F'G'$ on the coordinate - plane, we can see that it is a 90 - degree counter - clockwise rotation around the origin $O$. Also, a 270 - degree clockwise rotation around the origin $O$ is equivalent to a 90 - degree counter - clockwise rotation.

Answer:

B. 90 degree counterclockwise rotation around point $O$
D. 270 degree clockwise rotation around point $O$