Look at the four triangles graphed below.

What is the name of the single transformation that takes triangle *A* to triangle *D*?

A.

rotation

B.

reflection across the *y*-axis

C.

reflection across the *x*-axis

D.

translation


To determine the single transformation that takes triangle *A* to triangle *D*, let's analyze the possible transformations:

1. **Rotation** would imply that triangle *A* rotates around a point (such as the origin), changing its orientation. Check if the triangles have the same orientation, but this isn't usually the case for rotations.
2. **Reflection across the y-axis** would flip the triangle horizontally, changing its x-coordinates to their opposites.
3. **Reflection across the x-axis** would flip the triangle vertically, changing its y-coordinates to their opposites.
4. **Translation** means shifting the triangle without rotating or flipping it, meaning it would remain congruent to itself and in the same orientation.

Without seeing the graph, I would first suggest checking if triangle *A* is flipped in relation to *D*. If neither is flipped, it's likely a **translation**.

So, the answer is likely **D. Translation**, assuming that triangle *A* and triangle *D* are congruent and in the same orientation.

If you have the graph available, I can provide more specific details.

Would you like me to explain these transformations in further detail?

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Here are 5 questions for further practice:
1. What transformation would occur if triangle *A* were flipped over the x-axis instead?
2. How can you describe a rotation mathematically using coordinates?
3. Can a translation ever result in a flipped image?
4. What happens to the coordinates of a shape when it undergoes a reflection across the y-axis?
5. How would you combine transformations to reflect and then translate a shape?

**Tip:** When identifying transformations, always check if the orientation of the figure changes, as this rules out certain transformations like translations.

Look at the four triangles graphed below. What is the name of the single transformation that takes triangle A to triangle D? A. rotation B. reflection across the y-axis C. reflection across the x-axis D. translation

Discover how to identify the transformation that maps triangle A to triangle D in this geometry problem. Learn about the types of transformations, including translation, rotation, and reflection. Suitable for students in Grades 8-10.

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