To determine the set of transformations that are applied to parallelogram ABCD to create A″B″C″D″, let's analyze the coordinates.

Original Parallelogram ABCD:

• $A(-4, 1)$
• $B(-3, 2)$
• $C(-1, 2)$
• $D(-2, 1)$

Transformed Parallelogram A″B″C″D″:

• $A''(-4, -1)$
• $B''(-3, -2)$
• $C''(-1, -2)$
• $D''(-2, -1)$

Step 1: Reflection Analysis

The points in the transformed parallelogram have the same x-coordinates but their y-coordinates have changed sign. This indicates a reflection over the x-axis.

Step 2: Rotation Analysis

After reflecting over the x-axis, the coordinates of the points would be:

• $A'(-4, -1)$
• $B'(-3, -2)$
• $C'(-1, -2)$
• $D'(-2, -1)$

These are exactly the coordinates of A″B″C″D″, which indicates that no further rotation is needed.

Conclusion:

The transformation applied is a reflection over the x-axis.

The correct choice is not listed among the provided options, but if the reflection over the x-axis was combined with any rotation, the coordinates would not match the final points. Therefore, the correct transformation is just a reflection over the x-axis without any additional rotation.

Would you like more details or have any questions? Here are some related questions:

1. What would the coordinates be if the parallelogram were rotated 180°?
2. How do you determine the result of a 90° counterclockwise rotation?
3. What happens to a figure's coordinates when reflected over the y-axis?
4. How can you combine multiple transformations, such as a reflection and a rotation?
5. What other transformations could produce the same final coordinates?

Tip: Understanding how reflections and rotations affect coordinates can help you quickly determine the correct transformation sequence.