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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?

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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.

Determine a series of transformations that would map Figure E onto Figure F.

This problem demonstrates how to map Figure E onto Figure F using a sequence of geometric transformations, including translation and rotation. Learn how to apply the correct translation and rotation to move one figure to another on a coordinate plane. Suitable for Grades 8-10.

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