Subjects geometry

Rotation Translation 8Ac1Dc

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1. The problem asks where to rotate a shape and where to place it. 2. To rotate a shape, you need a point called the center of rotation. 3. Common centers of rotation are the origin $(0,0)$ or any specific point on the plane. 4. The rotation is described by an angle $\theta$, which tells how much to turn the shape around the center. 5. To place the shape, you translate it by moving every point by a certain vector $(h,k)$. 6. The combined transformation can be written as: first rotate around the center, then translate. 7. For example, rotating around the origin by $\theta$ degrees and then translating by $(h,k)$ moves point $(x,y)$ to: $$ (x',y') = (x\cos\theta - y\sin\theta + h, x\sin\theta + y\cos\theta + k) $$ 8. Without specific details, the general answer is: choose the rotation center (often the origin), rotate by the desired angle, then translate to the desired position.