https://file.aiquickdraw.com/mathbot/file/1733846154485bct0pmcb.jpg

The question asks which transformations carry the given regular polygon (a hexagon) onto itself. Let us analyze the options:

1. **Rotation of 300° clockwise**:  
   A hexagon is symmetric and can be rotated by multiples of \(360°/6 = 60°\) to map onto itself. A 300° clockwise rotation is equivalent to \(360° - 300° = 60°\) counterclockwise, which maps the hexagon onto itself.  
   ✅ Correct.

2. **Reflection across \(\ell\)**:  
   Regular polygons are symmetric along their axes of symmetry. The line \(\ell\) shown in the image appears to be one such axis of symmetry for this hexagon. Reflecting across \(\ell\) maps the hexagon onto itself.  
   ✅ Correct.

3. **Rotation of 300° counterclockwise**:  
   A 300° counterclockwise rotation is equivalent to \(360° - 300° = 60°\) clockwise. As previously established, rotations by multiples of 60° map the hexagon onto itself.  
   ✅ Correct.

4. **Rotation of 120° clockwise**:  
   Rotating the hexagon by 120° clockwise (which is \(2 \times 60°\)) is another valid transformation because it corresponds to one-third of a full rotation, which maps the hexagon onto itself.  
   ✅ Correct.

Thus, all the listed transformations carry the hexagon onto itself.

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Would you like more detailed explanations?  

### Related Questions:
1. What are the general rules for symmetries of regular polygons?  
2. How can you determine the number of lines of symmetry for a regular polygon?  
3. Why does a 300° clockwise rotation match a 60° counterclockwise rotation?  
4. Can any irregular polygon have the same rotational symmetry as a regular hexagon?  
5. How is reflection symmetry connected to rotational symmetry in polygons?

### Tip:  
For regular polygons with \(n\) sides, rotations by \(360°/n\) and reflections across axes of symmetry are always valid transformations that map the shape onto itself.

Which of the following transformations carry this regular polygon onto itself?

Explore the symmetry transformations of a regular hexagon, including rotations and reflections. Learn how transformations such as 300° clockwise rotation, reflection across an axis, and 120° clockwise rotation map the polygon onto itself. Suitable for Grades 9-12.

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