Rotation 180 Degrees: Symmetric Transformations of Polygons and Solids

①This example demonstrates rotating a planar polygon by 180 degrees about a point to obtain a symmetric figure, and also shows the application of rotation to 3D solids (cylinder, cuboid), scatter plots, and piecewise functions.②The core mathematical concept is rotational transformation, specifically central symmetry (180-degree rotation), involving angles, rotation center, congruence of figures, and coordinate transformations.③Construction highlights: using GeoGebra commands such as Polygon, Intersect, Segment, Rotate, CircleArc, and Angle; objects include original points (R,Q,P, etc.) and rotated points (R',Q',P', etc.), the rotated polygon poly1', as well as cylinder, cuboid, and scatter plot elements.④Suitable for middle school geometry teaching to visualize central symmetry and rotation, and also for introductory analytic geometry or computer graphics in university to understand coordinate rotation formulas.