To map Figure $F$ onto Figure $G$, we need to perform a series of geometric transformations. These can include translations, rotations, reflections, or dilations.

Let's break down the process by analyzing the given image:

1. Translation: The first step seems to be translating Figure $F$ downward, as Figure $G$ is located below the x-axis. The vertices of Figure $F$ are centered around $( -6, 7 )$, while the vertices of Figure $G$ are centered around $(-6, -3)$. The vertical displacement between these two centers is $7 - (-3) = 10$. So, a translation of 10 units downward should be applied.

2. Reflection: After translation, it looks like a reflection across the x-axis is necessary because Figure $G$ appears to be an upside-down version of Figure $F$. Reflecting the shape across the x-axis would invert it.

In summary, the sequence of transformations is:

• Translate Figure $F$ downward by 10 units.
• Reflect the figure across the x-axis.

Would you like further details on how these transformations work, or do you have any specific questions?

Here are 5 related questions for further exploration:

1. What is the algebraic formula for translating a figure on a coordinate plane?
2. How does reflection across the x-axis affect the coordinates of a figure?
3. What other transformations (e.g., rotation) could be applied to achieve the same result?
4. How can we represent these transformations as matrices for linear algebra applications?
5. What are the differences between reflection across the x-axis and the y-axis?

Tip: Always break down complex transformations into smaller steps for better understanding and precision.