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.