Q:

What are non-coplanar points in a plane?

A:

Non-coplanar points are any group of points that do not lie along the same geometrical plane. Points are considered coplanar if they lie along the same plane, and are often used to name that plane (e.g. plane ABCD). If a point E does not lie on plane ABCD, point E is non-coplanar with the other points. Points A, B, C and D are coplanar.

While an individual point has no characteristics, when grouped, points can become collinear, non-collinear, coplanar, or non-coplanar. Any two points have a line that runs through them, and are therefore automatically collinear. To get a non-collinear point, a third point that lies not on the line of the first two is needed. This point is non-collinear with the first two. However, in the same way that any two points are collinear, any three points are automatically coplanar, as it takes three points to define a plane. A fourth point is coplanar with this plane if it also lies in the same plane, and non-coplanar if not. It is collinear with at least one point, and coplanar with at least two, but in reference to the established plane, if the fourth point lies outside, it is considered non-coplanar.


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