To determine the series of transformations that would map Figure $U$ onto Figure $V$, we need to analyze the position, orientation, and size of both figures.

From the image, here's the initial assessment:

1. Reflection: It appears that Figure $V$ is a mirror image of Figure $U$. A reflection across the y-axis seems plausible because the shape is reversed horizontally.

2. Translation: After reflecting across the y-axis, Figure $U$ needs to be moved (translated) to the right so that it overlaps with Figure $V$. Specifically, we can estimate the translation by comparing the corresponding points of both figures.

3. No Rotation or Dilation: The size and orientation of the figure remain consistent after the reflection and translation, so there is no need for rotation or dilation.

Transformation Series:

1. Reflection across the y-axis.
2. Translation to the right by a certain number of units (estimated based on the coordinates of both figures).

Would you like a more detailed step-by-step analysis of the transformations, including calculations of specific coordinates and translations?

Here are 5 related questions:

1. What is the formula for reflecting a point across the y-axis?
2. How do you calculate the translation needed for a point on a coordinate plane?
3. Can reflections be combined with rotations? If so, how?
4. How would a dilation affect the figure in terms of size and orientation?
5. How can we distinguish between a translation and a rotation visually?

Tip: When determining transformations, always check if the figure's size changes to see if dilation is involved.