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Q: What is through any two points in geometry?

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Two dimensional geometry.

Yes, two points are always collinear. You can draw a line through any two points.

In plane geometry, the shortest distance between two points is a line. In spherical geometry, the shortest distance between two points is a segment of a great circle. The distance between one point and another is known as the displacement.

If the points are on the same line then are collinear.

In plane geometry, the shortest distance between two points is a line. In spherical geometry, the shortest distance between two points is a segment of a great circle. The distance between one point and another is known as the displacement.

Related questions

In plane geometry there is exactly one straight line through two points. There can be any number of curved lines.

In Euclidian or plane geometry, there can be only one line through two fixed points. Lines cannot actually be drawn; if you see it it is not a geometric line. If the points are on a curved surface as in a geometry that is non-Euclidian, then there can be infinitely many lines connecting two points.

In Euclidean geometry each line contains a minimum of an infinite number of points. In projective geometry, though, a line may have as few as two points.

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

Two end points.

In plane Euclidean geometry, only onle line can go through two distinct points.

Any two points are always collinear, since you can draw a straight line passing through any two points.

the line in geometry is a line segment that never ends

Not necessarily. There need not be in projective geometry, for example.

Elliptical geometry is like Euclidean geometry except that the "fifth postulate" is denied. Elliptical geometry postulates that no two lines are parallel.One example: define a point as any line through the origin. Define a line as any plane through the origin. In this system, the first four postulates of Euclidean geometry hold; through two points, there is exactly one line that contains them (i.e.: given two lines through the origin, there is one plane that contains them) and so on. However, it is nottrue that given a line and a point not on the line that there is a parallel line through the point (that is, given a plane through the origin, and a line through the origin, not on the plane, there is no other plane through the origin that is parallel to the given plane).

Two dimensional geometry.

A line

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