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One example I can think of is if you have two parallel lines - A and B
Every point on the line A is non-collinear to every point on line B
I don't know if this is what your prof. was thinking of or not.
But that's my guess.
(If this is what he / she is after, it is a bit of a trick question, IMHO. And as an answer to your first question, could a degenerate line consist of one point???)
If you think of it, let me know if any of this is what your prof. was after.
Thanks and
Good Luck!!
Answer this Question: "points, lines. sounds boring but dont let that stop you!"
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Points, lines. sounds boring but dont let that stop you!
 



Points, lines. sounds boring but dont let that stop you!
can a line have just one point?
the direction is two draw a figure fit to this description:
two points that are non collinear