Q: Through any two distinct points there exists exactly one line?

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Yes

Collinear points

There is exactly one line that can pass through two distinct points. This line is uniquely determined by the two points.

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.

Unique line assumption. There is exactly one line passing through two distinct points.

No, it is not true. Just think of the three vertices of a triangle.

== == Through any two points there is exactly one straight line.

A CD, because it exists in our dimension, has three distinct points you can measure therefor it is a cylinder.

A CD, because it exists in our dimension, has three distinct points you can measure therefor it is a cylinder.

Infinitely many if the 3 distinct points are collinear. Otherwise just 1.

A line that passes through a circle at two distinct points is called a secant.

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