In this problem, you are tasked with determining the series of transformations that would map Figure $S$ onto Figure $T$.

Step 1: Reflection

Looking at the graph, Figure $S$ and Figure $T$ seem to be symmetric across the x-axis. Therefore, the first transformation would be a reflection over the x-axis. This step would move Figure $S$ above the x-axis.

Step 2: Translation

After reflecting Figure $S$ over the x-axis, we still need to align it with Figure $T$. This can be done by translating the reflected figure.

After reflection, the shape will appear in the upper left quadrant. To map it exactly onto Figure $T$, you would need a translation to the right (along the x-axis) by 10 units and upward by 8 units.

Final Transformations

1. Reflection over the x-axis.
2. Translation: Right by 10 units and Up by 8 units.

Would you like further clarification or details?

Here are 5 related questions:

1. What is the effect of a reflection over the y-axis?
2. How do you determine the direction and distance of a translation?
3. Can rotations be used to achieve the same result in this problem?
4. What other transformations could be applied to Figure $S$ to achieve similar results?
5. How would you describe a dilation, and how does it differ from a translation?

Tip:

Always apply transformations step by step and check the intermediate result before moving to the next transformation.