To map Figure I onto Figure J, we need to analyze the geometric transformations involved. The following steps will describe how this transformation can be done:

1. Reflection:

• Reflect Figure I over the x-axis. This flips the figure, making its orientation match that of Figure J.

2. Translation:

• Translate the reflected figure up by 10 units and to the right by 6 units. This will move the figure from its current position to the position of Figure J.

Transformation Summary:

• Step 1: Reflect over the x-axis.
• Step 2: Translate by the vector (6, 10).

This series of transformations should map Figure I perfectly onto Figure J.

Would you like more details or have any questions?

Relative Questions:

1. How do you mathematically describe a reflection over the x-axis?
2. Can any other series of transformations achieve the same result?
3. What is the general rule for translating a figure in the coordinate plane?
4. How can you determine if two figures are congruent after transformations?
5. What happens to the orientation of a figure after a reflection?

Tip:

Always verify transformations by checking if corresponding points on the pre-image and image match up after each transformation.