The problem asks to identify the transformation that turns Figure $P$ into Figure $Q$.

Analysis:

• Figure $P$ is located in the second quadrant, and Figure $Q$ is located in the third quadrant.
• Both figures have the same size and orientation but are positioned differently on the coordinate plane.

By visual inspection, it seems that Figure $P$ was reflected across the x-axis. This reflection brings Figure $P$ down into the third quadrant, matching the position of Figure $Q$. The orientation of the vertices remains consistent, which confirms a reflection, not a rotation or translation.

Conclusion:

The transformation is a reflection over the x-axis.

Would you like further details or have any questions?

Here are 5 related questions for deeper understanding:

1. How does a reflection over the y-axis differ from a reflection over the x-axis in terms of transformation results?
2. What other transformations could lead to a similar result?
3. What happens to the coordinates of a point when it is reflected over the x-axis?
4. How would you describe a translation in mathematical terms?
5. Can a reflection and a translation achieve the same result? Why or why not?

Tip: When identifying transformations, pay attention to how coordinates of key points change after the transformation!