1. The problem statement, all variables and given/known data 4a) If x, y are in R, prove that (R, +) acts on R2 by (x,y)*r = (x+r, y) for all (x,y) in R2 and for all r in R. b) If (x,y) are in R2, find the orbit of (x,y). Describe geometrically. 2. Relevant equations none that I can think of 3. The attempt at a solution The group action part is easy. I have problems with (b). Am I supposed to just give the definition of the set (I don't think so). The set of orbits, geometrically, seems to be the set of all points (x,y) in R2.