Yes, three points determine a plane unless they are in a straight line.
A plane is two dimensions a line is only one.
You need a third point(not in the line) to define a plane.
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The shape described is a plane, which is a two-dimensional surface that extends infinitely in both width and length. In geometry, a plane can be uniquely determined by any three non-collinear points on the plane. This is known as the "three-point" or "unique determination" property of a plane. The three points define the plane's orientation and position in three-dimensional space.
Yes, three points define a plane. So any three points lie in some specific plane and are therefore co-planar.
Points that lie on the same plane are coplanar. Generally, three points have to be coplanar, but more than that can be in any plane.
Any three points that are non-collinear (not on the same line) will determine a plane.
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.