Dilations Exploration by Lance Bledsoe

① This example illustrates how shapes such as polygons and spheres are transformed under a dilation, highlighting the relationship between original and scaled figures. ② Core mathematical concepts include dilation (scaling), similarity, perimeter scaling, exponentiation, and the three‑dimensional effects of dilation on spheres. ③ Construction highlights: GeoGebra commands Polygon, Intersect, and Line are employed to build the original polygon (poly1) and its dilated version (poly2); objects A, B, C, D, a, b, c, d, etc., represent vertices, while A′, B′, C′, D′ denote the transformed points. The intersection of lines and polygons is calculated to verify similarity. ④ Aimed at middle‑school to high‑school students (grades 7‑12) studying geometry transformations, it also serves as an interactive visual aid for teachers and classroom demonstrations on scaling and similarity.