Randomized Reflection Worksheet Generator for Polygons in Coordinates

This example demonstrates how to generate a reflection (mirror) worksheet in an interactive way by randomizing input points. A polygon is created from randomly produced coordinates, then a corresponding reflected polygon (or related reference points) is constructed so learners can visually verify symmetry relationships and study how statistical characteristics change under random trials. Key math concepts include geometric transformation by reflection, polygon vertex coordinates, and supporting arithmetic/coordinate computations that can be connected to probability & statistics ideas such as confidence intervals. In GeoGebra construction, the Random command supplies randomized elements, while Polygon is used to build polygon objects from points (e.g., a, b, c, d, e, f, g, h) and from additional related points used for the reflected or comparison geometry (e.g., A, B, C, D, q1, a_1, b_1, c_1, d_1). Objects like l1 and text1 display results, and button1/button2/button3 provide controls to generate, update, or switch worksheet states. Suitable for secondary school through introductory university geometry, and also for exploratory learning in probability/statistics visualization.