Geometric Transformations of Triangles and Polygons Using Matrices

This GeoGebra applet demonstrates geometric transformations of triangles and polygons using matrices and linear functions. By constructing points, segments, and polygons, along with midpoints and intersections, it visually illustrates the application of linear algebra in geometric transformations. Users can observe the original and mapped figures to deeply understand how matrix operations affect the shape, position, and relationships of plane geometry figures. This applet allows interactive manipulation of transformation matrices, enabling students to explore common transformations such as translations, rotations, reflections, and scaling in real time. As users adjust matrix parameters, they can immediately see how the corresponding linear mappings reshape the displayed figures on the coordinate plane. The applet also highlights key geometric properties preserved or altered during transformations, such as collinearity, ratios of distances, and angle relationships. This hands-on exploration strengthens the connection between abstract algebraic computations and concrete geometric intuition, making it an effective teaching tool for bridging linear algebra and Euclidean geometry. Students benefit from immediate visual feedback, which supports discovery-based learning and helps solidify their understanding of how matrices serve as powerful tools for describing and analyzing geometric changes. The inclusion of midpoints and intersection points further enriches the experience by allowing learners to investigate invariant properties and confirm theoretical results experimentally.