To map Figure $E$ onto Figure $F$, you would need to apply a sequence of transformations. Let's analyze the transformations step by step:

1. Translation: Notice that Figure $F$ is to the left of Figure $E$, and slightly lower. The first step could be translating Figure $E$ left and downwards to match the position of Figure $F$. You can calculate the exact translation by finding the distance between a specific point on Figure $E$ and its corresponding point on Figure $F$.

2. Rotation: After translating, we can see that Figure $F$ is rotated counterclockwise compared to Figure $E$. You may need to apply a rotation by a specific angle (likely 90°, 180°, or another value) around a certain point (possibly the origin or the centroid of one of the figures) to align the orientation.

3. Reflection (if needed): It does not appear that Figure $E$ needs to be reflected to match Figure $F$, but you should confirm this by checking if the two figures are mirror images along a particular axis.

The most likely transformations are a translation followed by a rotation.

Would you like me to help calculate the exact translation and rotation, or do you want to explore these transformations interactively?

Here are 5 related questions that can expand on this topic:

1. How do you determine the exact distance needed for translation between two points?
2. What is the difference between a clockwise and counterclockwise rotation in transformations?
3. How do you calculate the angle of rotation needed to map one figure onto another?
4. When is a reflection necessary in geometric transformations?
5. How can you combine multiple transformations, such as translation and rotation, efficiently?

Tip: When translating, pay attention to the coordinates of specific points on both figures to ensure accurate movement.