https://file.aiquickdraw.com/mathbot/file/17261862343008huakp4s.jpg

The image shows a coordinate grid with a transformation of triangle GHI to G'H'I'. Let's analyze the options provided to determine the correct answer based on the information shown in the graph.

### Observations from the Graph:

1. **Triangles GHI and G'H'I':** 
   - The original triangle GHI is larger and positioned above the x-axis.
   - The transformed triangle G'H'I' is smaller and positioned below the x-axis.
   - The triangles appear to share the same center of dilation, which is the origin (0,0).

2. **Characteristics of Transformation:**
   - **Similarity:** The shape and orientation of triangle G'H'I' resemble triangle GHI, indicating a similar figure.
   - **Dilation:** The transformation reduces the size of the triangle, meaning it is a dilation with a scale factor less than 1.
   - **Congruence of Segments:** The corresponding segments of GHI and G'H'I' are not congruent as G'H'I' is smaller than GHI.

### Analyzing the Answer Choices:

1. **The image is smaller than the pre-image.**
   - This is true since triangle G'H'I' is smaller than triangle GHI.

2. **Triangle GHI is similar to Triangle G'H'I'.**
   - This is also true because dilation maintains the similarity of figures.

3. **The transformation shown is a dilation.**
   - This is correct, as the transformation reduces the size while preserving the shape.

4. **Segment GH is congruent to segment G'H'.**
   - This is incorrect because the segments of G'H'I' are not congruent to GHI's; they are proportionally smaller.

### Conclusion:
- The correct answers are:
  1. The image is smaller than the pre-image.
  2. Triangle GHI is similar to Triangle G'H'I'.
  3. The transformation shown is a dilation.

Would you like more details or have any questions?

### Related Questions:
1. What is the difference between a dilation and a reflection in geometry?
2. How do you determine the scale factor of a dilation on a coordinate grid?
3. What properties of a triangle are preserved under dilation?
4. How do you find the center of dilation for a transformation?
5. What are the rules for transformations in coordinate geometry?

**Tip:** When working with dilations, always check for the center of dilation and the scale factor to determine the nature of the transformation.

The image is smaller than the pre-image. Triangle GHI is similar to Triangle G'H'I'. The transformation shown is a dilation. Segment GH is congruent to segment G'H'.

This problem involves analyzing the transformation of Triangle GHI to G'H'I' on a coordinate plane. The problem covers key concepts in coordinate geometry and transformations, particularly dilation and triangle similarity. Suitable for students in Grades 8-10.

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