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Q: Any three points lie on a distinct line?

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No, because Of any three points on a line there exists no more than one that lies between the other two.

It takes exactly 2 distinct points to uniquely define a line, i.e. for any two distinct points, there is a unique line containing them.

A.True

False!

Yes

In a Euclidean plane any two distinct points uniquely define a straight line.

1. Given any line, there are at least two points on the line. Call them A and B. 2. Given any line, there exists at least one point in the plane that is not on the line. Call that point C. 3. Given any two points (A and C and, then B and C) there exists a straight line joining them. The point C is not on AB so AB and AC are distinct. Similarly, AB and BC are distinct so that there are three lines that meet, in pairs, at three vertices - and that is a triangle.

Any three points which do not form a line.

Through any three points NOT on the same straight line. If they are all on the same line then that line can act as an axis of rotation for an infinite number of planes containing the three points.

No, given any three points, it is possible for one of the points not to be on the line defined by the other two points. Only two points on a line are needed to identify the exact position of the line. The positions of any three points gives you the exact position of the plane that includes those three points.No, it is not true. If it were true, all triangles would be straight lines !?!

You have to have three or more points to have non-colinear points because any two points determine a line. Noncolinear are NOT on the same line.

Any three points that are non-collinear (not on the same line) will determine a plane.

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