Translation Investigation: Dynamic Triangle Transformation with Vectors

This example demonstrates how to perform translation transformations on triangles using vectors. Core mathematical concepts include translation transformation, vector operations, and similarity. Construction details: Use the Polygon command to draw the original triangle ABC, define a translation vector v with the Vector command, apply the Translate command to create translated points A', B', C', and draw the translated triangle; set up text input boxes for users to customize vector coordinates (v_x, v_y) for interactive dynamic demonstration; display the distance between point A and its translated point A' using the Distance command to help students intuitively understand that corresponding points are connected by equal and parallel segments after translation. Suitable for middle school geometry teaching to aid understanding of translation transformations and vector applications in geometry.