1. **Problem Statement:** We need to find a series of transformations that map Figure R, located in the bottom-right quadrant (positive $x$, negative $y$), onto Figure S, located in the top-left quadrant (negative $x$, positive $y$). 2. **Understanding the Quadrants:** Figure R is in quadrant IV (where $x>0$ and $y<0$), and Figure S is in quadrant II (where $x<0$ and $y>0$). 3. **Transformation Strategy:** To move a figure from quadrant IV to quadrant II, we can use reflections or rotations. 4. **Reflection about the y-axis:** Reflecting Figure R about the y-axis changes the sign of the $x$-coordinates but keeps $y$ the same. This moves the figure to quadrant III (where $x<0$, $y<0$). 5. **Reflection about the x-axis:** Reflecting the result about the x-axis changes the sign of the $y$-coordinates but keeps $x$ the same. This moves the figure from quadrant III to quadrant II (where $x<0$, $y>0$). 6. **Summary of transformations:** - Reflect Figure R about the y-axis: $(x,y) \to (-x,y)$ - Then reflect about the x-axis: $(-x,y) \to (-x,-y)$ 7. **Check final position:** After these two reflections, the figure is in quadrant II, matching Figure S. 8. **Alternative single transformation:** A rotation of 180 degrees about the origin also maps quadrant IV to quadrant II by sending $(x,y) \to (-x,-y)$. **Final answer:** The series of transformations is either: - Reflect Figure R about the y-axis, then about the x-axis, or equivalently, - Rotate Figure R 180 degrees about the origin.