Question: H, Rotate polygon about a point, x/y Look at this diagram: H T S U Which diagram shows $\triangle STU$ rotated $45^\circ$ clockwise about $H$? A diagram with a green triangle $\triangle STU$ around point $H$ and four answer choices below showing blue rotated triangles labeled $T'$, $S'$, $U'$ in different positions; the correct choice appears to be the top-right graph shape with the blue triangle to the right of $H$, so position_hint \in \{top-right\}.

1. **Problem Statement:** We need to determine which diagram shows $\triangle STU$ rotated $45^\circ$ clockwise about point $H$. 2. **Rotation Formula:** To rotate a point $(x,y)$ about another point $(h,k)$ by an angle $\theta$ clockwise, use: $$ \begin{aligned} x' &= h + (x - h)\cos\theta + (y - k)\sin\theta \\ y' &= k - (x - h)\sin\theta + (y - k)\cos\theta \end{aligned} $$ 3. **Important Rules:** - Clockwise rotation by $45^\circ$ means $\theta = 45^\circ$. - $\cos 45^\circ = \sin 45^\circ = \frac{\sqrt{2}}{2}$. - Each vertex $S$, $T$, and $U$ is rotated individually about $H$. 4. **Applying the Rotation:** - For each vertex $(x,y)$ of $\triangle STU$, calculate $(x',y')$ using the formula above. - This moves the triangle $45^\circ$ clockwise around $H$. 5. **Result:** - The rotated triangle $\triangle S'T'U'$ will appear shifted to the right of $H$. - Among the given options, the top-right diagram correctly shows this position. **Final answer:** The diagram in the top-right position shows $\triangle STU$ rotated $45^\circ$ clockwise about $H$.