Enlargement and Reduction of Figures (Homothety)

This GeoGebra applet demonstrates the enlargement and reduction of plane figures, specifically homothety (dilation) in geometry. By constructing a polygon and its vertices, the Dilate command is used to generate the scaled polygon. Users can visually observe the geometric properties of homothetic figures, such as the lines connecting corresponding points intersecting at a single point called the center of homothety, and the corresponding sides being parallel and proportional. The applet allows students to adjust the scale factor dynamically, observing how positive and negative scale factors affect the orientation and size of the transformed figure. When the scale factor is greater than one, the figure enlarges; when it is between zero and one, the figure reduces. A negative scale factor produces a reversed image on the opposite side of the center of homothety. This interactive environment is designed for middle and high school geometry instruction, helping students build a deep conceptual understanding of homothety, including its defining properties: preservation of angle measures, proportionality of corresponding side lengths, collinearity of corresponding points with the center, and the consistent ratio between distances from the center to corresponding vertices. Students can manipulate the position of the center of homothety and the scale factor to explore how these parameters influence the transformation, making abstract geometric relationships tangible and observable. The applet serves as an effective teaching and learning tool for visualizing one of the fundamental transformations in Euclidean geometry.