1. The problem asks to identify which transformation of triangle $\triangle ABC$ is a rotation of $30^\circ$ about point $P$. 2. A rotation transformation involves turning a figure around a fixed point (called the center of rotation) by a certain angle and direction (clockwise or counterclockwise). 3. Key properties of rotation: - The center of rotation remains fixed. - The figure's shape and size remain unchanged. - The orientation is preserved (no flipping). 4. From the descriptions: - Top-left: $\triangle A'B'C'$ is rotated counterclockwise about $P$ by about $30^\circ$. - Top-right: $\triangle A'B'C'$ is rotated clockwise about $P$ by about $30^\circ$ but orientation is flipped (not a pure rotation). - Bottom-left: $\triangle A'B'C'$ is translated (moved without rotation). - Bottom-right: $\triangle A'B'C'$ is rotated counterclockwise about $P$ by about $30^\circ$ with orientation preserved. 5. Since a rotation must preserve orientation and be about point $P$ by $30^\circ$, the correct transformation is the one described in the bottom-right position. **Final answer:** The transformation in the bottom-right graph is a rotation of $30^\circ$ about point $P$.