# Point (geometry)

fundamental object of geometry: locus within which we can distinguish no other locus than itself

A point is a position in space which has no size, but which does have position.

In geometry, a point has no size, but has a position. This means it has no volume, area or length. We usually draw a point as a small cross 'X' or a small dot (a small, round shape). Different points can be labelled using capital letters (A, B, C...X, Y, Z).[1][2] The point is one of the most fundamental ideas in geometry.[3]

Two points form a line segment. When part of a line segment, the points are called its vertices. All polytopes are made of vertices.

In general, two points can be:

• Coincident (they are one and the same, such as on coinciding lines)[4]
• Not coincident (they are not one and the same)

and are always:

• Coplanar (on the same plane)
• Colinear (on the same line)
• Concyclic (on the same circle)

Three points can be:

• Colinear
• Coincident
• Not coincident
• Not colinear

and are always:

• Coplanar
• Concyclic

Four points can be:

• Coplanar
• Colinear
• Coincident
• Not coincident
• Not colinear
• Not coplanar

## References

1. "List of Geometry and Trigonometry Symbols". Math Vault. 2020-04-17. Retrieved 2020-09-24.
2. "Point - math word definition - Math Open Reference". www.mathopenref.com. Retrieved 2020-09-24.
3. "Points, Lines, and Planes". www.cliffsnotes.com. Retrieved 2020-09-24.
4. "Coincident Lines (Definition, Equation & Example)". BYJUS. Retrieved 2024-08-19.