Word Count : 372

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To perform continuous rotation of a hexagon about an arbitrary point ((x₀, y₀)), follow these steps: 1. Define the Hexagon Vertices: Let the hexagon vertices be (P_1(x_1, y_1), P_2(x_2, y_2), \dots, P_6(x_6, y_6)). 2. Translate Hexagon to Origin: To rotate about ((x₀, y₀)), first translate the hexagon so that ((x₀, y₀)) becomes the origin: [ x_i' = x_i - x₀, \quad y_i' = y_i - y₀ ] 3. Apply Rotation Matrix: For rotation by an angle (\theta) (in radians), the 2D rotation matrix is: [ \begin{bmatrix} \cos\theta & -\sin\theta \ \sin\theta & \cos\theta _________ _______ ________ __________ ______ __________.
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