The given polygons suggest a sequence of rigid transformations.

1. Step 1: Polygon 1 (ABCD) is reflected across the x-axis. This is because the coordinates of Polygon 1 in Quadrant II (negative x, positive y) are transformed to Quadrant IV (negative x, negative y), indicating a reflection over the x-axis.

2. Step 2: The second reflection results in the transformation of the points further within Quadrant IV. A reflection across the y-axis would not produce the observed coordinates of Polygon 2 (A'B'C'D'), but instead, a reflection across the line y = -x achieves this. The points are mirrored in such a way that the new coordinates match.

Thus, the correct sequence of transformations is:

• A reflection across the x-axis, followed by
• A reflection across the line y = -x.

Does that answer help clarify the problem for you? Here are five related questions:

1. What is the definition of a rigid transformation in geometry?
2. Can two reflections across different axes ever be equivalent to a single transformation? If so, when?
3. How can you determine which axis or line a polygon was reflected over, just from its coordinates?
4. What happens to the coordinates of a point after reflecting it over the line y = x?
5. How do reflections affect the orientation of a shape?

Tip: When reflecting a point across the x-axis, its y-coordinate changes sign while the x-coordinate remains the same.