When you have three collinear points there is one gradient. I'm not sure what your question is specifically but when points are collinear they have the same gradient.
I think you mean: Are any three points contained in exactly one plane? only if they're not collinear... I think
3 non-collinear points define one plane.
The definition of a non-collinear line is that this is a line on which points do not lie on one line. The opposite of this is a collinear point. Collinear points refer to three points that do fall on a straight line.
Only one if they are non-collinear. An infinite number if they are collinear.
If three points all lie on the same line, then the points are said to be "collinear". This is also true if the slope from each point to the next is the same.
yes
Collinear points
Exactly one.
Exactly one.
I think you mean: Are any three points contained in exactly one plane? only if they're not collinear... I think
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.
Exactly one. No more and no less.
3 non-collinear points define one plane.
As long as at least two of them are different points, exactly one line.
Yes, it is true that through any three points, if they are not collinear (not all lying on the same straight line), there exists exactly one line that can be drawn through any two of those points. However, if the three points are collinear, they all lie on the same line, meaning that there is still only one line that can be associated with them. In summary, the statement holds true under the condition that the points are not all collinear.
Three non-collinear points always define exactly one and only one plane. That's why a 3-legged table or chair never wobbles.
The definition of a non-collinear line is that this is a line on which points do not lie on one line. The opposite of this is a collinear point. Collinear points refer to three points that do fall on a straight line.