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Q: What kind of points determine a plane?

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Any 3 points determine a plane.

Three non-linear points determine a plane.

No. Three points do. Two points determine a line.

three points can determine a plane

No, 2 points define a line, 3 points define a plane.

No. If the four points are coplanar, they determine only one plane!

A plane

Three points can determine a plane but not 3-d space.

Any three points that are non-collinear (not on the same line) will determine a plane.

Any 3 points

Any 4 points can lie in a plane, 3 points determine a plane and just take the 4th to be say the origin.

Yes.

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