Dilation2: Scale Factors and Segment Ratios

This example visualizes how a dilation (proportional scaling) transforms key points and figures, and how the dilation scale factor determines the ratio between corresponding segment lengths. It focuses on the geometric phenomenon that corresponding distances change in a predictable way under similarity transformations. The main concepts include dilation, scale factor, corresponding points/segments, and measurable length ratios (using intersections and connected segments as geometric structure). Construction in GeoGebra uses Point and Polygon to create the initial configuration, Dilate to generate the mapped counterparts (e.g., A′, B′, D′), Segment to draw corresponding edges between original and image points, and Distance to measure lengths and derive the ratio relationships. Parameters (such as t and scale-related variables) together with text labels (text1–text3) help present and verify the computed scale-factor effects. Suitable for middle school geometry through early high school, and useful for interactive lessons on similarity, transformations, and ratio-based reasoning.