Q: How many points are necessary to define a line?

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There is only one line (or line segment) that can be drawn between two distince points.

In classical or Euclidean plane geometry two points defines exactly one line. On a sphere two points can define infinitely many lines only one of which will represent the shortest distance between the points. On other curved surfaces, or in non-Euclidean geometries, the number of lines determined by two points can vary. Even in the Euclidean plane, two points determine infinitely many lines that are not straight!

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Only two are necessary to define a line. But infinitely many are required to DRAW it.

They define one plane. A line is defined by two points, and it takes three points to define a plane, so two points on the line, and one more point not on the line equals one plane.

Two.

a line has to have at least 2 points.a plane has to have at least 3 points.______________It takes two points to define a unique line in Euclidean space. But every line and every line segment contains infinitely many points. The same is true for planes in Euclidean space. You need at least 3 points to define a unique plane, but every plane containes infinitely many points and infinitely many lines or line segments.

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.

There are no planes containing any number of given points. Two points not the same define a line. Three points not in a line define a plane. For four or more points to lie in the same plane, three can be arbitrary but not on the same line, but the fourth (and so on) points must lie in that same plane.

4 points define a plane.

A line has infinitely many subsets, not just three. Any collection of points on the line constitute a subset.

Infinitely many. There are infinitely many points in the plane and although any pair of points define a line, no matter how many lines you are given, it is always possible to find a point that is not on any of them - that is, a point that is not collinear.

A line segment consists of an infinite number of points. Depending on how you define "breaking it down", yes, it's possible. But of course not in a finite number of steps.

A line has an infinite amount of points.

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