Composition of Translations = Vector Addition: Dynamic Demo

① This example demonstrates that composing two translations is equivalent to adding their corresponding vectors, by applying successive translations to an image. ② The core mathematical concept is vector addition and the composition property of translations: translating by vector u then by vector v yields the same result as a single translation by vector w = u + v. ③ Construction details: using GeoGebra commands Vector to create vectors u and v, and Translate to translate image1 to image1' and image1''; objects include image1, image1', image1'', points A, B, C, D, E, E', and vectors u, v, w, z. ④ Suitable for middle school to high school students learning vectors and geometric transformations, and for teachers to illustrate the geometric meaning of vector addition and composition of translations.