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To map Figure \( J \) onto Figure \( K \), we can analyze the transformations by comparing the orientation, position, and size of both figures. Here's a step-by-step approach to determine the series of transformations:

1. **Reflection**:
   - First, notice that Figure \( J \) and Figure \( K \) are mirror images of each other with respect to the x-axis. This suggests that a reflection over the x-axis is the first transformation.

2. **Translation**:
   - After reflecting, Figure \( J \) would be below the x-axis, similar to the position of Figure \( K \). Next, we observe that Figure \( J \) must be translated to the right and downward to match the exact position of Figure \( K \).
   - Specifically, the translation should move the figure 2 units to the right and 4 units down.

### Transformation Sequence:
1. **Reflect** Figure \( J \) over the x-axis.
2. **Translate** the reflected figure 2 units to the right and 4 units down.

These transformations will map Figure \( J \) onto Figure \( K \).

Would you like any further details on this solution? Here are some related questions you might find helpful:

1. What is the general formula for reflecting a point over the x-axis?
2. How can you determine the translation vector between two figures?
3. What are some common sequences of transformations used in geometry?
4. How does the orientation of a figure change after reflection?
5. How do you prove that a sequence of transformations is correct?

**Tip:** When working with transformations, always check the final position and orientation of the figure to ensure that the transformations were applied correctly.

Determine a series of transformations that would map Figure J onto Figure K.

Learn how to determine a series of transformations that map Figure J onto Figure K. This problem involves key geometric concepts, including reflection and translation, and is suitable for students in Grades 6-8.

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