Using your transparency, show that under a sequence of any two translations, Translation and Translation, (along different vectors), that the sequence of the Translation followed by the Translation, is equal to the
sequence of the Translation, followed by the Translation. That is, draw a figure, A, and two vectors. Show that
the translation along the first vector, followed by a translation along the second vector, places the figure in the same
location as when you perform the translations in the reverse order. (This fact is proven in high school Geometry.)
Label the transformed image A'. Now, draw two new vectors and translate along them just as before. This time,
label the transformed image A". Compare your work with a partner. Was the statement "the sequence of the
Translation followed by the Translation, is equal to the sequence of the Translation, followed by the
Translation" true in all cases? Do you think it will always be true?