all of them are collinear they lie in the same plane
lie on the same plane and are collinear
No. For any three points it is always possible to find a plane on which they all lie. A fourth point is most unlikely to be coplanar with the first three unless it is deliberately placed to be so.
Yes, they are.
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They need not be. The four vertices of a quadrilateral are coplanar but NOT collinear. On the other hand, any line (in Eucledian geometry) has an infinite number of points on it - all of which are coplanar.
all of them are collinear they lie in the same plane
Three points are, but not four.
No, they always are From Wikipedia.org, "The World's Encyclopedia" when I searched coplanar In geometry, a set of points in space is coplanar if the points all lie in the same geometric plane. For example, three distinct points are always coplanar; but four points in space are usually not coplanar. Since 3 points are always coplanar. A point and line are always coplanar
The answer depends on the number of point. One point - as the question states - cannot be non-collinear. Any two points are always collinear. But three or more points will define a plane. If four points are non-coplanar, they will define four planes (as in a tetrahedron).
If they lie in the same plane.
lie on the same plane and are collinear
No. For any three points it is always possible to find a plane on which they all lie. A fourth point is most unlikely to be coplanar with the first three unless it is deliberately placed to be so.
No. If the four points are coplanar, they determine only one plane!
No. A trinagle does not require four points, three are sufficient. And any three points, if they are not colinear, must be coplanar.
Yes, they are.
Yes, they are.