Translating Geometric Objects by Vector <a,b>

This GeoGebra example demonstrates how to translate geometric objects using vector <a,b>. The core mathematical concept is vector-based translation and its coordinate representation. Construction points: 1) Create base geometric objects (triangles, polygons, or points); 2) Define translation vector <a,b> using Vector command or slider parameters; 3) Apply Translate command to move the original object to its image; 4) Observe the positional relationship and attribute changes before and after translation. Suitable for middle school mathematics lessons on translation or GeoGebra beginner tutorials, helping students intuitively understand vectors as tools that determine translation direction and distance.