Point (geometry)

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A point is a 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). In geometry, points are always labelled by capital letters (A, B, C...X, Y, Z).

Mathematicians say 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

Compare: line, plane