Fraction and 2D Vector Problem Solving

This example demonstrates the use of GeoGebra to construct geometric models involving fractions, 2D vectors, rectangles, spheres, tree diagrams, and orthocenters to solve related mathematical problems. The core math concepts include fraction operations, 2D vector representation and manipulation, analytical geometry of rectangles and spheres, probability and statistics via tree diagrams, and the geometric concept of the orthocenter. The construction highlights the use of LaTeX commands for text display, creation of points A, B, C, and multiple text objects (text1 to text12) for labeling and explaining geometric elements. Suitable for high school students learning analytical geometry, vectors, and probability statistics, as well as for mathematical competitions or teaching demonstrations.