Matrix Rotation and Inequality-Constrained Point Sequence with Dilation

This example demonstrates how a sequence of points is dynamically generated and transformed under matrix rotation, inequality constraints, and dilation controlled by sliders. The core mathematical concepts include matrix transformations (rotation), vector operations, inequality regions, sequence generation, and homothety (dilation). Construction highlights: using GeoGebra commands Point, Vector, Textfield, and Sequence to create base objects such as points a_n, vector u, texts text1/text2, and input box inputBox1; sliders k, h, n control parameters; define function f and initial point x_0; generate multiple transformed points (A2 to A10, B2 to B10) via sequences, forming list1 and associated points I1, J1, K1, L1, A1. Suitable for high school or early college students to explore how matrix rotation and scaling affect point sets, how inequality regions restrict point distributions, and the geometric meaning of dilation and homothety.