Question

figure f is the result of a transformation on figure e. which transformation would accomplish this? answer a rotation 90° counterclockwise about the origin a rotation 90° clockwise about the origin a translation 5 units right and 4 units up a translation 4 units right and 5 units up

Explanation:

Step1: Analyze rotation rules

For a 90 - degree counter - clockwise rotation about the origin, the transformation rule for a point $(x,y)$ is $(-y,x)$. For a 90 - degree clockwise rotation about the origin, the rule for a point $(x,y)$ is $(y, - x)$. For a translation $a$ units right and $b$ units up, the rule for a point $(x,y)$ is $(x + a,y + b)$.

Step2: Check translation

If we consider the translation options:

• For a translation 5 units right and 4 units up, if a point on Figure E is $(x,y)$, the new point is $(x + 5,y+4)$.
• For a translation 4 units right and 5 units up, if a point on Figure E is $(x,y)$, the new point is $(x + 4,y + 5)$.
• By observing the coordinates of corresponding points of Figure E and Figure F, we can see that if we take a point on Figure E, say $(0,- 4)$, moving it 5 units right and 4 units up gives $(0 + 5,-4 + 4)=(5,0)$ which is consistent with the transformation from Figure E to Figure F.
• Rotation 90 - degree counter - clockwise and clockwise about the origin will change the orientation of the figure in a way that is not consistent with what is shown.

Answer:

A translation 5 units right and 4 units up