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Q: If three points are coplanar are they also collinear?

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Yes, they are.

true

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.

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

Two points are collinear if there is a line going through them. A higher-dimensional counterpart to this is "coplanar": objects are coplanar if there is a plane that contains the objects. There's always a plane containing any three points, so you'd need at least four points (in at least three dimensions) for this distinction to be meaningful. However, it's also possible to discuss two or more coplanar lines, for example - if two lines are not coplanar, they are called skew. To visualize this, imagine a bridge crossing a river: the bridge and the river could be extended into lines that are not contained in any common plane. Beyond coplanar objects, it's possible to discuss "cospatial" objects that lie in the same three-dimensional space. However, you'd need at least four dimensions to even talk about this, since in three dimensions everything is cospatial, in a way. Another related concept to collinear is "concurrent." This refers to three or more lines (or circles) that all intersect at the same point.

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no.

Yes, collinear points are also coplanar.

True.

not necassarily

Yes, they are.

Yes, they are.

true

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.

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

Yes. Three co-linear points define a line, and therefore also lie on a plane, but those three points do not necessarily define only one plane. You need three points, not co-linear, to uniquely define a plane. See Related Links below for more information.

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.

A point or, if the lines are also collinear, the line(s).

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