Zig Zag: Vector-Based Polyline with Geometric Transformations

This example demonstrates a dynamic 'Zig Zag' pattern that starts from the origin and is constructed using vectors, orthogonal lines, and sequences, resulting in a polyline with adjustable parameters for intuitive control. The core mathematical concepts include 2D vectors, straight lines and perpendicularity, geometric transformations (such as translation and rotation), piecewise functions, and congruence. Construction highlights: using GeoGebra commands such as Vector, OrthogonalLine, Sequence, PolyLine, and Segment, with objects including points A, B, C, vector u, parameters m and n, and lists list1, bpts, apts, list4. The pattern is built by generating a sequence of points and connecting them with polylines, while orthogonal lines enforce right-angle relationships. Suitable for high school or early college students learning vectors, transformations, and dynamic geometry, and for exploring how parameter changes affect the shape, fostering visual intuition.