hmmm...there seems to be a lot of theory missing from your question.

By "pick one point in group B and check the p-value" what do you mean? How will testing one point tell you if group B as a whole belong's to group A? And what exactly do you mean by "belong"? That it follows the same statistical model? Also, how do you know that the points in group A follow a linear model?

sorry for the confusion.

pick one point in group B and check the p-value" what do you mean?

pick one point in group B and calculate the possibility it follows the same statistical model of group A

How will testing one point tell you if group B as a whole belong's to group A? And what exactly do you mean by "belong"? That it follows the same statistical model?

test one point and tell if this point follows the same statistical model of group A.

Also, how do you know that the points in group A follow a linear model?

I have lots of points and the linear model fits well. I can try to use some other models to fit the data, but my point is "after that, how can I tell whether another point follows the same statistical model or not"

Thanks