Geometric Transformations: Translation, Reflection & Rotation

① This example visually demonstrates three fundamental geometric transformations—translation, reflection, and rotation—by applying them to a triangle in a dynamic GeoGebra worksheet. ② Core mathematical concepts include geometric transformations, vectors, axes of symmetry, rotation centers, and congruence of transformed figures, with additional references to sine functions, frequency distribution, and centroid. ③ Construction details: The original triangle (triangle1) is created using the Polygon command, a translation vector is defined with the Vector command, and the translated triangle (triangle2) is generated via the Translated object. Auxiliary points and lines (Point, Horizontal, Vertical) help set up reflection and rotation axes, while transformed edges (c', a', b') are displayed. ④ This resource is ideal for middle and high school geometry classes, math labs, or self-study, helping students visualize transformation properties and explore combined transformations.