Triangle Rotation 699F71

1. **Problem Statement:** Identify which diagram shows $\triangle UVW$ rotated $30^\circ$ counterclockwise about point $V$. 2. **Understanding Rotation:** A rotation of $30^\circ$ counterclockwise about point $V$ means that point $V$ remains fixed, and points $U$ and $W$ move along circular arcs centered at $V$ by $30^\circ$ in the counterclockwise direction. 3. **Key Rule:** The center of rotation ($V$) does not move. 4. **Analyzing Each Diagram:** - **Top-left:** $V'$ is to the right of $V$, $W'$ near the top, and $U'$ near left-middle. This matches a $30^\circ$ counterclockwise rotation about $V$ because $U$ and $W$ have moved counterclockwise around $V$. - **Top-right:** $V'$ is at upper-left, which means $V$ moved, so this cannot be a rotation about $V$. - **Center:** $V'$ is at right-middle, so $V$ moved, not fixed. - **Bottom-right:** $V'$ is at lower-right, so $V$ moved. 5. **Conclusion:** Only the **top-left** diagram shows $\triangle UVW$ rotated $30^\circ$ counterclockwise about $V$. **Final answer:** Top-left diagram.