Combine Transformations

You can combine transformations. For instance, first translate and then rotate an image. If you always translate and rotate by the same amounts, what path will the feet take? Do you get the same result if you rotate first and then translate? When you combine two or more different kinds of transformations, which transformations have to be done in a certain order and which combinations are the same in any order? Can you get the same result with a rotation about a point as with a translation followed by a reflection?