(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

4a) If x, y are inR, prove that (R, +) acts onR2 by (x,y)*r = (x+r, y) for all (x,y) inR2 and for all r inR.

b) If (x,y) are inR2, 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) inR2.

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# Homework Help: For (x,y) in R2, describe the set of orbits geometrically.

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