affine sets in $\mathbb{R}^2$

Question

I was trying to visualize all affine sets in $\mathbb{R}^2$.

I started with single points. All points are affine sets of cardinality one.

Now I thought of adding another point to the context. The set of two points is not affine. But the affine hull is a line through these points which is an affine set.

Now, I thought of adding a point which is not in the line . The union of line and the new point is not affine. The affine hull cor this union set is $\mathbb{R}^2$.

So the affine sets are {singleton points ,lines, $\mathbb{R}^2$}

Is this right?