Vectors and Hyperbola: Coordinate Statistics under Geometric Transformations

This GeoGebra example demonstrates the construction of a hyperbola-related figure using vector tools, integrating geometric transformations with coordinate statistics. The core mathematical concepts include the definition and properties of hyperbolas, vector representation and translation, coordinate systems, and geometric transformations such as translation and rotation. The construction uses the Vector command to create vector u, defines points P and Q, and generates text objects text1, text2, and text3 to display coordinates or statistical characteristics. This example is suitable for high school or early college students to understand the role of vectors in geometric construction, how to combine algebraic coordinates with geometric figures, and to foster dynamic exploration and mathematical modeling skills.