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Q: What would happen if three collinear points are used to define a plane?

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No, they have to be noncolinear, that is they all can't be on the same line.

I dont think that "If four points are collinear they are also coplaner," is the same thing as "If four points are coplaner they are also collinear,". The definition of collinear is at least three points on the same line. To define a plane is to have threenoncollinear points.

To create a plane, infinitely many. But to uniquely define one, 3 are enough.

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.

The points are collinear, and there is an infinite number of planes that contain a given line. A plane containing the line can be rotated about the line by any number of degrees to form an unlimited number of other planes.If, on the other hand, the points are not collinear, then the plane has no wriggle room: it is stuck fast in one place - there can be only one plane containing all the points. Provided they are non-colinear, three points will define a plane.

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Yes. You require three non-collinear points to uniquely define a plane!

No, they have to be noncolinear, that is they all can't be on the same line.

I dont think that "If four points are collinear they are also coplaner," is the same thing as "If four points are coplaner they are also collinear,". The definition of collinear is at least three points on the same line. To define a plane is to have threenoncollinear points.

Any three non-collinear points will define a single plane. A plane is composed of an infinite number of distinct lines.

Yes. In fact any three points that are not collinear define a plane and therefore MUST lie on a plane.

Infinitely many. There are infinitely many points in the plane and although any pair of points define a line, no matter how many lines you are given, it is always possible to find a point that is not on any of them - that is, a point that is not collinear.

Points that are collinear will be located on the same line. A line is a subset of a plane. Therefore, Yes, points that are collinear will be located on the same plane.

Three non-collinear points always define exactly one and only one plane. That's why a 3-legged table or chair never wobbles.

To create a plane, infinitely many. But to uniquely define one, 3 are enough.

3 non-collinear points define one plane.

Here is one option: 2 points uniquely define a line so a line can be named after any two points that belong to it. Similarly, three points that are not collinear (all in the same line) uniquely define a plane so a plane can be defined by naming any three non-collinear points in it. There are different - though related - forms in coordinate geometry or in vector algebra.

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