Reflection and Rotation: Dynamic Geometric Transformations with Complex Numbers

This GeoGebra example dynamically demonstrates how planar figures change under reflection (Mirror) and rotation (Rotate) transformations, vividly illustrating the geometric essence of symmetry and rotational motion. Core mathematical concepts include reflection, rotation, complex number representation, and composition of transformations, with extensions to cosine, variance, and piecewise functions. The construction uses Line to define axes, Mirror to create reflected images (e.g., pic1'), Rotate to generate rotated objects (pic1'', A', A''), and Segment with Angle to mark key segments and the rotation angle α, resulting in an interactive scene with points A, B, C, D, E, f, g, h. This is suitable for upper secondary or early university students to explore the algebraic representation and graphical correspondence of geometric transformations, and serves as a valuable resource for mathematics laboratory activities.