https://file.aiquickdraw.com/mathbot/file/1729858650125at3bl57m.jpg

Looking at the transformation in the image, we see that the green triangle \( \triangle DEF \) has been transformed into the orange triangle \( \triangle ABC \).

- The green triangle appears to be reflected over the \( y \)-axis, as the points switch horizontally across the \( y \)-axis. For example, point \( D(-4, 5) \) is reflected to point \( A(4, 1) \).
- Then, there is a dilation (size change) involved. The triangles do not preserve their size after the reflection. Specifically, the green triangle is larger, and after the reflection, the orange triangle is a scaled-down version of it.

Thus, the correct answer for the composition of transformations is **Dilation and Reflection**.

Would you like more details on any specific part of this transformation?

Here are five related questions to further explore the topic:
1. How can you mathematically represent a reflection over the \( y \)-axis?
2. What is the formula for a dilation, and how does it affect coordinates?
3. How can you determine the scale factor of a dilation?
4. Can a composition of transformations include more than two types of transformations?
5. How would the result change if the reflection happened over the \( x \)-axis instead?

**Tip:** When dealing with compositions of transformations, it’s useful to follow the path of one key point to understand the sequence of movements.

What composition of transformations took place?

Understand the composition of transformations involving dilation and reflection. In this problem, a triangle undergoes reflection over the y-axis followed by dilation. Learn the key mathematical concepts and formulas used in this transformation geometry problem. Suitable for Grades 7-10.

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