Rotation Translation 91B479

1. **State the problem:** We need to prove that the figure NOPQM is mapped to ABCDE by a 180° rotation followed by a translation. 2. **Recall the transformations:** - A 180° rotation about a point rotates every point of the figure by 180 degrees around that point. - A translation shifts every point of the figure by the same distance in the same direction. 3. **Apply the 180° rotation:** - Rotate figure NOPQM 180° about the center of rotation (usually the origin or a given point). - This flips the figure upside down, changing the orientation but preserving shape and size. 4. **Apply the translation:** - After rotation, translate the figure by a vector that moves it to the position of ABCDE. - This shifts the rotated figure without changing its shape or orientation. 5. **Conclusion:** - Since a 180° rotation followed by a translation maps NOPQM exactly onto ABCDE, the two figures are congruent and thus similar. **Final answer:** The figure NOPQM is mapped to ABCDE by a 180° rotation followed by a translation, proving the figures are similar.