To determine which transformation carries the trapezoid onto itself, we need to analyze the options provided and the position of the trapezoid on the graph.

Analysis:

The trapezoid is positioned on the graph with vertices at specific points. The key to solving this is to recognize which line the trapezoid can be reflected over so that it maps onto itself.

1. Reflecting over the line $y = -3$:
   This line is horizontal and located at $y = -3$. The trapezoid seems to be symmetric with respect to this line, meaning that reflecting over $y = -3$ would map the trapezoid onto itself.

2. Other Reflection Options:

   • Reflecting over $y = 3$: This line is too far above the trapezoid, and a reflection over it would not carry the trapezoid onto itself.
   • Reflecting over $x = 3$ or $x = -3$: These lines are vertical, and reflecting over them would move the trapezoid to a different position.

Conclusion:

The correct transformation that carries the trapezoid onto itself is the reflection over the line $y = -3$. This is consistent with the symmetry of the trapezoid relative to this line.

Would you like more details on transformations or symmetry? Here are five related questions you might find interesting:

1. How do you find the line of symmetry for other geometric shapes?
2. What is the general rule for reflecting a point over a given line?
3. Can reflection always map a shape onto itself?
4. How can you determine if a shape has multiple lines of symmetry?
5. What other transformations can map a shape onto itself?

Tip: When identifying a line of symmetry, check if the shape mirrors itself perfectly when folded along that line.