https://file.aiquickdraw.com/mathbot/file/172894263614076s0dm1k.jpg

The image shows two squares, \(FGHI\) and \(F'G'H'I'\), plotted on a coordinate plane. Square \(FGHI\) is located in the third quadrant, while square \(F'G'H'I'\) is in the first quadrant.

To determine which transformation maps \(FGHI\) onto \(F'G'H'I'\), we need to consider the possible transformations such as translation, reflection, rotation, or dilation.

### Observing the Graph:

- The shape and orientation of both squares are identical, which suggests that no rotation or reflection has occurred.
- The squares seem to be positioned symmetrically across the origin, implying a **translation**.
  
We can verify this by checking the coordinates of corresponding points on both squares.

For example:
- \( F (-7, -8) \) maps to \( F' (3, 2) \)
- \( G (-5, -8) \) maps to \( G' (5, 2) \)

### Calculating the Translation:
From \( F (-7, -8) \) to \( F' (3, 2) \), the translation is:

\[
T(x, y) = (x + 10, y + 10)
\]

This means that each point in \(FGHI\) is translated 10 units to the right and 10 units up to form \(F'G'H'I'\).

Thus, the transformation that maps \(FGHI\) onto \(F'G'H'I'\) is a **translation by 10 units to the right and 10 units up**.

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Do you have any questions or need further details? Here are five follow-up questions that can extend the discussion:

1. What is the general formula for a translation on a coordinate plane?
2. How can you verify whether a transformation includes a reflection?
3. What other transformations could have been applied if the squares were different sizes?
4. How do you calculate a translation vector between two points?
5. What happens if we combine translation with rotation or reflection?

**Tip**: Always check corresponding points when trying to identify a transformation!

Which of the following transformations maps square FGHI onto square F'G'H'I'?

Learn how to determine the correct transformation that maps square FGHI onto square F'G'H'I' using translation techniques on a coordinate plane. This detailed problem covers geometric transformations, including translation by a vector. Suitable for students in Grades 8-10.

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