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# Point (geometry)

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A **point** is a precise position in space. Imagine touching a piece of paper with a sharp pencil or pen, without making any sideways movement. We know where the point is, but it has no size to speak of.

In geometry, a point has no size, but has a position. This means it has no volume, area or length. We usually represent a point by a small cross 'X' or by a small **dot** (a small, round shape). Points are always labelled by capital letters (A, B, C...X, Y, Z).^{[1]}^{[2]} It is one of the most fundamental but undefined terms in geometry.^{[3]}

In general, **two points** can be:

- Coincident (they are one and the same)
- 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

## Related pages

## References

- ↑ "List of Geometry and Trigonometry Symbols" (in en-US). 2020-04-17. https://mathvault.ca/hub/higher-math/math-symbols/geometry-trigonometry-symbols/.
- ↑ "Point - math word definition - Math Open Reference". https://www.mathopenref.com/point.html.
- ↑ "Points, Lines, and Planes". https://www.cliffsnotes.com/study-guides/geometry/fundamental-ideas/points-lines-and-planes.