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There are infinitely many points in a plane.
A minimum of three points are required to define a plne (if they are not collinear). And in projective geometry you can have a plane with only 3 points. Boring, but true. In normal circumstances, a plane will have infinitely many points. Not only that, there are infinitely many in the tiniest portion of the plane.
a plane is any plane surface it usually have 3 or 4 points * * * * * You need only three points provided they are not collinear. And most planes have infinitely many points although there are geometries with only a finite number of points.
4 points define a plane.
A plane can be determined by three points, as long as the three points do not lie along a single line.