Ch 16 Problem 2: Reflection Points and Orthocenter on One Line

This example demonstrates the geometric phenomenon that in a triangle, the three reflection points obtained by reflecting each vertex across its opposite side, together with the orthocenter, lie on a single straight line. The core mathematical concepts involve the orthocenter of a triangle, reflection transformations, and collinearity. Construction details: using GeoGebra commands such as Polygon to construct triangle ABC, Circle for the circumcircle, Point for vertices, Mirror to reflect vertices across opposite sides producing points D, D', etc., Line to connect relevant points, OrthogonalLine to construct altitudes, and Intersect to find the orthocenter E. By observing the collinearity of the reflection points and the orthocenter, the theorem is verified. Suitable for high school geometry courses or competition mathematics when studying orthocenter properties and reflections, and also useful as a dynamic geometry exploration example.