Point (geometry)

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

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.