1. The problem asks which transformations create trapezoid W'X'Y'Z' congruent to trapezoid WXYZ. 2. The given options include combinations of translations, rotations, and reflections. 3. To determine the correct transformations, consider the positions of the trapezoids: WXYZ is in the lower-right quadrant, and W'X'Y'Z' is in the upper-left quadrant. 4. A rotation of 180° about the origin moves points from one quadrant diagonally opposite, changing $(x,y)$ to $(-x,-y)$. 5. A reflection across the y-axis changes $(x,y)$ to $(-x,y)$, flipping the figure horizontally. 6. A reflection across the x-axis changes $(x,y)$ to $(x,-y)$, flipping the figure vertically. 7. A rotation of 90° clockwise about the origin changes $(x,y)$ to $(y,-x)$. 8. Since W'X'Y'Z' is in the upper-left quadrant and WXYZ is in the lower-right, a rotation of 180° about the origin moves WXYZ to the upper-left quadrant. 9. However, the orientation of W'X'Y'Z' compared to WXYZ suggests a reflection is also involved. 10. Reflecting the rotated trapezoid across the y-axis changes the orientation to match W'X'Y'Z'. 11. Therefore, the transformations used are a rotation of 180° about the origin and a reflection across the y-axis. 12. This matches the third option: "rotation of 180° about the origin and a reflection across the y-axis."