There's lots of study guides on the web as well as books in the library. Checking out the requirements isn't too hard. For instance, is there a 0 vector? Yes, (0,0) satisfies the + requirement. Test this by (0,0) + (x,y) = (x,y) in your addition scheme. Now, is there an inverse to (x,y)? Try (-x,-y). And keep on going for every requirement. The only strange thing about your multiplication by a scalar is that the y coordinate seems to be mapped to 1 for all y.