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Points all in one plane?
Two dimensional geometry.
Can there be four points in one plane?
There can be any number of points on a plane, or even on a line - and any number of lines on a plane.
Is it true that three points are always contained in exactly one plane?
3 points must always be contained in one plane, as 2 make a line, it makes no difference as to where the third point is, it will exist in the same plane in the two. Aside from all three points being in a line, this is always true.
What three points determine a pane?
Any 3 geometric points, as long as they are all in different locations and not superimposed on each other, will define a plane. In other words, there is only one plane that can pass through 3 distinct points. If you had only two points, it would define a line, but not a plane. A plane can include 2 points but if there are only 2 that are specified, the plane can rotate around those 2 points, generating infinitely many planes.
Which geometric object is defined as the set of all points in a plane that are equidistant from one point?
Parabola - apex
