The problem asks to determine a series of transformations that would map Figure $J$ onto Figure $K$ based on the diagram. Let's analyze the necessary transformations.

Observations:

• Figure $J$ is located in the second quadrant.
• Figure $K$ is located in the fourth quadrant.
• Both figures are triangles, but they appear to be reflections or rotations of each other.

Transformation Steps:

1. Reflection across the x-axis: This will flip Figure $J$ from the second quadrant to the fourth quadrant, similar to where Figure $K$ is located.

   • Reflection rule: $(x, y) \mapsto (x, -y)$.

2. Translation: After reflecting Figure $J$, it might not be perfectly aligned with Figure $K$. A translation may be needed to shift the figure into place.

   • Based on the diagram, Figure $J$ can be shifted a few units horizontally and vertically to match Figure $K$.

I can provide a more detailed calculation or description if needed. Would you like me to go into more detail about the reflection and translation process?

Here are 5 follow-up questions for you:

1. What are the coordinates of the key vertices of Figures $J$ and $K$?
2. How does reflection affect the orientation of the figure?
3. Would a rotation be another valid transformation to consider here?
4. What are the rules for translating a shape on the coordinate plane?
5. How can we check if two figures are congruent after transformation?

Tip: Always perform one transformation at a time, then check the result on the coordinate plane before proceeding to the next step.