Geometric Inversion of a Quadrilateral

This GeoGebra applet demonstrates geometric inversion in the plane. Users can drag the vertices of a general quadrilateral to dynamically observe its image under a circle of inversion. Utilizing commands like Polygon, Segment, and Sequence, the construction visually illustrates how inversion mapping affects the shape and boundaries of polygons, aiding in the understanding of conformal properties and mapping behavior in inversive geometry. The applet features an adjustable inversion circle whose radius and center can be modified, allowing learners to explore how the position and size of the circle influence the resulting transformed figure. As vertices are manipulated, the image quadrilateral updates in real time, showing how sides that do not pass through the center of inversion are mapped to circular arcs, while sides passing through the center are mapped to lines. This interactive visualization reinforces key concepts such as the fact that inversion preserves angles (conformality) and maps generalized circles to generalized circles. Students can use this tool to develop intuition about a transformation that is fundamental in advanced Euclidean geometry, complex analysis, and hyperbolic geometry, turning abstract definitions into concrete, observable relationships.