Locus Exploration with Circle and Rotation Transformations

This GeoGebra example demonstrates geometric construction involving circles and locus generation under rotation transformations. By defining fundamental objects such as points, segments, polygons, and circle arcs, it uses the Rotate and Locus commands to explore the path characteristics of points undergoing rotational motion. Concepts include central angles, circle sectors, and vectors, making it an effective visual tool for teaching rotation symmetry and trajectory equations in plane geometry. Students can dynamically manipulate parameters such as the angle of rotation, the position of the center point, and the shape of the generating figure to observe how the locus changes in real time. The interactive nature of the applet allows learners to build intuition about how rotational transformations affect geometric figures and how loci are formed through continuous motion. This hands-on exploration supports deeper understanding of the relationship between angular displacement, arc length, and the resulting curve traced by a point. The applet is particularly suitable for classroom demonstrations or self-directed study, helping students connect abstract algebraic descriptions of curves with their geometric origins.