The question asks for transformations (translations, rotations, and reflections) that would take Polygon P (the green one) to Polygon Q (the blue one). Let's go through each of the options to determine if they are correct.

1. Translate so that A is taken to J. Then rotate 120° clockwise around point D.

   • This involves moving Polygon P so that point A matches point J, followed by a 120° clockwise rotation around point D.
   • This transformation seems plausible, as the rotation would align the two polygons. This is a valid transformation.

2. Reflect over DX.

   • A reflection over the line DX would flip the polygon across the line DX. However, this would not map Polygon P onto Polygon Q. This is not a valid transformation.

3. Rotate 180° counterclockwise around D and reflect over AD.

   • A 180° counterclockwise rotation around D would position the polygon upside down, and a reflection over line AD would then flip it. This seems to correctly map Polygon P onto Q. This is a valid transformation.

4. Rotate 120° clockwise around point D.

   • A 120° clockwise rotation around point D without any translation seems to work in aligning Polygon P with Q. This is a valid transformation.

5. Reflect over CD and rotate 60° clockwise around point D.

   • A reflection over line CD followed by a 60° clockwise rotation around D does not align Polygon P with Q. This is not a valid transformation.

Conclusion:

The correct transformations are:

• Translate so that A is taken to J. Then rotate 120° clockwise around point D.
• Rotate 180° counterclockwise around D and reflect over AD.
• Rotate 120° clockwise around point D.

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

1. What is the mathematical definition of a reflection?
2. How do you calculate the result of a 120° rotation in a coordinate plane?
3. What is the process of combining transformations like translation and rotation?
4. How does a reflection over a line affect the orientation of a shape?
5. Can any sequence of transformations map any polygon to another congruent polygon?

Tip: When performing a series of transformations, visualize each step independently to ensure the final position aligns with the target shape.