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Four points are always coplanar if?
all of them are collinear they lie in the same plane
If four points are collinear they are also coplanar?
Yes, since any line can be contained in a plane.
Four points are always coplanar if they?
lie on the same plane and are collinear
Can four points be collinear?
Yes. On any straight line you can find an infinite set of 4 points which are collinear.
What is a two or three dimensional counterpart of a collinear?
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.
