To map Figure E onto Figure F, we can break down the transformations step by step based on the image provided. Let's analyze the positioning of both figures.

1. Rotation:

   • Notice that Figure F appears to be a rotated version of Figure E. If you rotate Figure E by 180 degrees around the origin (0,0), it would closely align with the orientation of Figure F.

2. Translation:

   • After rotating Figure E, the resulting figure is still not in the exact position as Figure F. We can apply a translation. Specifically, we need to translate the figure so that it shifts to the correct position. By moving the figure 7 units to the right and 8 units up, it aligns with Figure F.

Transformation Steps:

1. Rotate Figure E by 180° around the origin.
2. Translate the rotated figure by 7 units right and 8 units up.

These transformations will map Figure E onto Figure F.

Would you like further details on how to perform these transformations, or do you have any questions?

Related questions:

1. What other types of transformations can be used to map figures?
2. How do you determine the correct rotation angle between two figures?
3. What is a translation, and how is it represented mathematically?
4. Can two figures be mapped using only a translation without rotation?
5. How do you verify if the transformation is correct?

Tip:

When determining transformations, start by identifying if a rotation or reflection is needed, and then handle translations as a final step to match the position.