13.3 Translate, Rotate, Reflect – Round 3 (Geometry Transformations)

This GeoGebra example demonstrates how a configuration of points and its polygonal shape change under three fundamental transformations: translation, rotation, and reflection. It emphasizes the visual correspondence between original and transformed elements and highlights invariants such as preserved distances/structure and consistent mapping relationships. Key math concepts include vector-based translation, rotation determined by direction/angle with distance preservation, reflection across a line, and the broader viewpoint of similarity transformation by tracking how geometric quantities relate. Construction-wise, the setup uses the GeoGebra commands Polygon and Vector, together with objects representing polygon vertices (A, B, C, D, E, F) and vectors (v, t1, t2) as transformation descriptors. Additional constructed entities (c, a, b, t1, t2, f, d, e) support circular references (e.g., unit-circle/circumcircle themes) or intermediate geometric parameters needed to drive the transformations. Suitable for middle-to-high school geometry, classroom demonstrations, and self-study of transformation mappings using dynamic geometry software.