Point vs. Point on a Line vs. Intersection

① This GeoGebra example visually distinguishes three types of points in geometric construction: a free point, a point constrained on a line or curve, and an intersection point of two objects. ② Core mathematical concepts include classification of geometric objects, point-line incidence, uniqueness of intersections, and logical dependency in constructions (e.g., whether a point is draggable or determined by other objects). ③ Construction details: Based on the summary, commands Line, Point, and Intersect are used, creating objects W, X, f, Y, Z, g, A, B, C. Points A, B, C likely represent intersections, while W, X, Y, Z are free or on-object points; comparing their draggability and properties reveals the differences. ④ Suitable for middle school to high school students learning geometric construction and logical reasoning, as well as for teachers demonstrating object dependencies and rigor in GeoGebra.