The image shows a series of triangles labeled 1, 2, and 3, along with a coordinate grid and the equation of the line $y = x$. The problem asks for the composition of transformations that took place, and four options are provided:

• Translation and Rotation
• Rotation and Reflection
• Reflection and Translation
• Translation and Dilation

Analysis:

1. From Triangle 1 to Triangle 2:

   • The transformation appears to involve a reflection across the line $y = x$. Triangle 2 is the mirror image of Triangle 1 across this diagonal line.

2. From Triangle 2 to Triangle 3:

   • The transformation looks like a translation, as Triangle 3 maintains its orientation and size but is shifted upward and to the right from Triangle 2.

Conclusion:

The composition of transformations is Reflection and Translation, making the correct answer the third option: Reflection and Translation.

Do you want further details on reflections and translations, or have any questions?

5 Related Questions:

1. How do you perform a reflection across the line $y = x$?
2. What is the difference between translation and dilation?
3. How do you determine if a transformation is a rotation?
4. Can a translation change the size of a shape?
5. What properties remain unchanged under a reflection?

Tip:

Always check if shapes maintain their size and orientation when identifying a translation, and whether they flip across a line for reflection.