
There are several rigid transformations that could take Polygon A to Polygon B. Choose **two** correct transformations below.

Group of answer choices

Reflection of A over the y-axis and then reflection over the x-axis

Translation down 4 and right 4

Rotation 180 degrees around the Center (0, 0)
 

To determine which transformations map Polygon A to Polygon B, we evaluate the choices based on the types of rigid transformations (translation, reflection, and rotation).

1. **Reflection of A over the y-axis and then reflection over the x-axis**:
   - Reflecting over the y-axis mirrors the figure horizontally, while reflecting over the x-axis mirrors it vertically. A combination of these two reflections effectively rotates the shape by 180 degrees about the origin. 
   - **This is a valid transformation**.

2. **Translation down 4 and right 4**:
   - This describes moving the entire polygon 4 units down and 4 units to the right.
   - **This is a valid transformation**.

3. **Rotation 180 degrees around the center (0, 0)**:
   - A 180-degree rotation around the origin changes the orientation of the shape but maintains its structure.
   - **This is a valid transformation**.

Since we need to select **two** correct transformations, the valid choices are:
- **Reflection of A over the y-axis and then over the x-axis**
- **Rotation 180 degrees around the Center (0, 0)**

Would you like further details or explanations? Here are five questions to explore the topic further:

1. What are other examples of rigid transformations?
2. How does a reflection differ from a rotation in terms of symmetry?
3. Can a translation be considered a rotation under certain conditions?
4. How do we distinguish between clockwise and counterclockwise rotations?
5. What is the difference between a rigid and non-rigid transformation?

**Tip**: Always ensure that transformations preserve distances and angles, as these are the characteristics of rigid transformations.

There are several rigid transformations that could take Polygon A to Polygon B. Choose two correct transformations below.

Group of answer choices:
- Reflection of A over the y-axis and then reflection over the x-axis
- Translation down 4 and right 4
- Rotation 180 degrees around the Center (0, 0)

Explore how to apply rigid transformations to map Polygon A to Polygon B, including reflections, translations, and rotations. This problem covers core geometric concepts and theorems, suitable for Grades 8-10.

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