One-Seventh Triangle Linear Transformation

This example demonstrates the geometric effect of a specific linear transformation on a right triangle, mapping its vertices proportionally to create an inner nested triangle that is one-seventh of the original area. The core mathematical concepts include linear transformations, matrix multiplication, similarity of triangles, and area ratios. Construction highlights: using GeoGebra commands such as Polygon to build the original right triangle, Segment and Intersect to create intersection points, and Textfield with InputBox to adjust transformation parameters interactively. Multiple associated triangles (e.g., A1, B1, C1) and their transformed images are generated to visualize the mapping. This resource is suitable for high school or early college students to intuitively grasp how linear transformations alter shape and area, and serves as a dynamic teaching aid for matrix transformations.