Showing that a non-empty subset M is an affine subset of R^4

Hi, I have to do a project on affine subsets and affine mappings, but I have no clue what they are... We are given only one clue and I can't find many notes on google. I would really appreciate it if someone could help me with this first problem (and if you could also give me a link to some good notes on the topic). Thanks a lot! :)

The problem says:

"To illustrate this concept, show that

and

is an affine subset of ."

And the only hint we get is

"Throughout Part A of this project, V will be a real vector space and, for a non-empty subset S of V and a V, the set { } will be denoted by S+a.

An affine subset of V is a non-empty subset M of V with the property that whenever and ."

Re: Showing that a non-empty subset M is an affine subset of R^4

OK, I have managed to solve the problem... I just have to substitute lambda*x+(1-lambda)*y into both of the conditions given. :)