Question

answer a rotation 180° counterclockwise about the origin a rotation 90° counterclockwise about the origin a translation 1 unit to the right and 1 unit up a rotation 90° clockwise about the origin submit answer

Explanation:

Step1: Recall rotation and translation rules

For a point $(x,y)$ rotated 180° counter - clockwise about the origin, the new point is $(-x,-y)$. For a 90° counter - clockwise rotation, the new point is $(-y,x)$ and for a 90° clockwise rotation, the new point is $(y, - x)$. For a translation 1 unit right and 1 unit up, a point $(x,y)$ becomes $(x + 1,y+1)$.

Step2: Analyze the transformation from Figure D to Figure E

If we take a vertex of Figure D, say $(0,-3)$.

• For 180° counter - clockwise rotation about the origin, $(0,-3)$ becomes $(0,3)$.
• For 90° counter - clockwise rotation about the origin, $(0,-3)$ becomes $(3,0)$.
• For 90° clockwise rotation about the origin, $(0,-3)$ becomes $(-3,0)$.
• For translation 1 unit right and 1 unit up, $(0,-3)$ becomes $(1,-2)$.

By observing the orientation and position of Figure D and Figure E, we can see that a 180° counter - clockwise rotation about the origin maps Figure D to Figure E.

Answer:

A rotation 180° counterclockwise about the origin