Translations: Translate and Then Translate Again

① This example demonstrates the effect of applying two successive translations to a polygon, showing that the final image is congruent to the original and that the combined transformation is equivalent to a single translation by the sum of the two vectors. ② Core mathematical concepts include translation transformations, vector addition, congruence, and the parallelogram law. ③ Construction details: The initial polygon is created with the Polygon command; two vectors are defined using the Vector command; the Translate command is applied twice to the polygon and its sides, producing intermediate and final images; Textfield and InputBox objects allow users to input vector components dynamically, making the construction interactive. Objects include polygon poly1, vectors u and v, translated polygons poly1' and poly1'', and corresponding edges and vertices. ④ Suitable for middle school to high school students learning geometric transformations, and for teachers demonstrating the composition of translations in class.