To prove that three points are colinear, pick two points and form the equation of the line they describe, and then see if the third point lies on that line.
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3 or more points are colinear when they all fall on the same line on the same plane.
colinear points
non collinear point or points? no collinear points are points not on the same line. keep in mind that you have to have at least 3 points to make that happen.
Colinear points mean that if you draw a (really long) line between any two of them, the line will pass through the others. Or simply: there can exist a straight line that can pass through all of them. These are colinear points: . .... .. One line can pass through all of them: These ar not colinear points: :. If I try to connect any two of them with a line, the third point will not lie on that line.
Any three points anywhere in space can be the vertices of a triangle, as long as all three are not colinear.