Its been a while, so I hope someone else chimes in on this to confirm or correct what I'm about to say, but any rigid motion can be expressed as a composition of rotations and translations.

Now,I'm right about that, then you can assume that is either a rotation or a translation because if its a composition, we can take it apart. For instance, if where is some rotation and is some translation, we can see that and from that point we can just worry about what happens to either the rotation or translation and then combine them later.IF

That said, my best guess as to what's being asked in this problem is just to say whattypeof motion is, and that's going to depend on what type of motion itself is.

Try thinking about it that way. You're going to basically answer two questions:

(1) What kind of motion is when is a rotation?

(2) What kind of motion is when is a translation?

One last hint: Based on my long-winded explanation up there, its either going to be a rotation, a translation, or a composition of a rotation with a translation in each case.