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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

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