It appears that you are now saying that plane \(\displaystyle \bf K\) in figure I contains all the given points.I have no idea how to go about this question. Would points GFC work?
Yes, I apologize! I will be sure to include the multiple-choice problems.It's important that you tell us the entire problem as given to you; that includes the list of options, if it is a multiple-choice problem.
I found this, contains the same question (#5): http://teachers.stjohns.k12.fl.us/jasper-k/files/2016/02/unit7-quiz-review-with-solutions.pdf
It's clear that all the points lie in the plane of the paper, so they are merely asking for a name of that plane.
K would be the best answer to give; but they are really asking, "Which of these is a valid name for the plane containing lines m and p?" There are many valid names; but the only one of the choices that works is GFC, since only that is a set of three non-collinear points in the plane (as you said in post #4).
This is an example of why I really dislike multiple-choice problems, unless they are written really well. Making it multiple-choice changes the very meaning of the problem! But this is also why you really must always include the choices when you ask about such a problem.