Enlarging and Reducing a Figure via Similarity Transformation

This example demonstrates how to enlarge or reduce a figure in the coordinate plane while preserving similarity: corresponding angles remain equal and corresponding side lengths scale by a constant similarity ratio. The key ideas include similarity transformations (scaling), the role of the scale factor, correspondence between original and transformed vertices, and how these geometric relations connect to trigonometric reasoning and quadratic-function/ parabola-related measurements. Construction highlights: GeoGebra uses Polygon to build the base polygonal figure, and Sequence to generate a structured set of points/parameters that produce the transformed vertices (objects such as A, B, C, D, q1, q2, q3, q4, q5 and mapped points like P, Q, R, S are created from ordered sequences). By parameterizing the point positions and applying the consistent similarity scale across the vertex set, the enlarged/reduced figures are constructed for direct comparison. Suitable for secondary-to-pre-university math instruction and for classroom activities focused on geometric transformation, similarity, and linking geometry to analytic representations.