Determine whether the two classes are linearly separable (algorithmically in 2D)

Question

There are two classes, let\'s call them X and O. A number of elements belonging to these classes are spread out in the xy-plane. Here is an example where the two classes are

Answer 1

Computing a linear SVM then determining which side of the computed plane with optimal marginals each point lies on will tell you if the points are linearly separable.

This is overkill, but if you need a quick one off solution, there are many existing SVM libraries that will do this for you.