https://file.aiquickdraw.com/mathbot/file/1727399937211iqqg8bqf.jpg

The question asks for the transformation that relates Figure \( I \) to Figure \( H \). From the image, we can analyze the transformation by comparing the positions of the two figures on the coordinate plane.

### Observations:
- Figure \( H \) is in the first quadrant, and Figure \( I \) is in the third quadrant.
- Both figures are triangles, and it appears that Figure \( I \) is an inverted version of Figure \( H \), but still has the same size and shape.
- The orientation of Figure \( I \) suggests it has undergone a reflection across the origin. This type of transformation is known as a **rotation by 180 degrees** about the origin.

### Explanation:
- **Rotation by 180°**: Rotating a figure by 180° about the origin maps the coordinates \((x, y)\) of each point in Figure \( H \) to \((-x, -y)\), which is what we observe in Figure \( I \).
  
Thus, the transformation that maps Figure \( H \) to Figure \( I \) is a **180° rotation** about the origin.

Would you like further details on how this type of transformation works or have any other questions?

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Here are five related questions to expand on this:
1. What is the general rule for a 90° rotation about the origin?
2. How does a reflection across the x-axis differ from a reflection across the y-axis?
3. What is the difference between a rotation and a reflection in terms of transformation?
4. How can you determine the transformation if both rotation and reflection are combined?
5. What are the possible effects of translating a figure after rotation?

**Tip:** A 180° rotation is a simple transformation because it always changes the signs of both the x and y coordinates, making it easy to identify when comparing figures.

Figure I is the result of a transformation on Figure H. Which transformation would accomplish this?

Understand the transformation that maps Figure H to Figure I through a 180° rotation about the origin. This problem explores key geometric concepts including transformations, rotations, and coordinate mapping, suitable for students in Grades 8-10.

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