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.