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Q: Any two points are contained in exactly one plane?
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Through any three points there is exactly one plane cointaining them?

I think you mean: Are any three points contained in exactly one plane? only if they're not collinear... I think


Is it true that any three points are contained in exactly one plane?

Yes, if you are talking about Euclidean geometry.


Could any two point be contained in exactly one plane?

Yes.No. Any two planes will be contained in infinitely many planes, not "exactly one".


Through any three points there exists exactly one plane?

Collinear points


Do planes contain exactly three points?

No. The tiniest piece of a plane contains an infinite number of points. But if you give us just three points, then we know exactly what plane you're talking about, and it can't be any other plane.


Are three noncollinear points always contained in only one plane?

Yes a plane can always be drawn three any three points, whether they are linear or not.


Through any two points there is exactly?

one plane LINE


If four points are collinear they are also coplanar?

Yes, since any line can be contained in a plane.


How many non-collinear points are there in one plane?

There are an infinite number of any kind of points in any plane. But once you have three ( 3 ) non-collinear points, you know exactly which plane they're in, because there's no other plane that contains the same three non-collinear points.


Through any three points not on a line there is one?

between two point there is exactly one line between three points there is exactly one plane


Is there exactly one line through two points?

In plane geometry there is exactly one straight line through two points. There can be any number of curved lines.


Can there be four points in one plane?

There can be any number of points on a plane, or even on a line - and any number of lines on a plane.