Introduction to Three-dimensional Geometry

Coordinates of a Point in Space


  • In three dimensions, the coordinate axes of a rectangular Cartesian co-ordinate system are '3' mutually perpendicular lines. The axes are called the x, y and z axes.
  • The three planes determined by the pair of axes are the coordinate planes, called XY, YZ and ZX-planes.
  • The three coordinates planes divide the space into eight parts known as octants.
  • The coordinates of a point p in the three dimensional geometry is always written in the form of triplet like (x, y, z). Here x, y and z are the distances from the YZ, ZX and XY-planes.
  • Any point on x-axis is of the form (x, 0, 0).
  • Any point on y-axis is of the form (0, y, 0).
  • Any point on z-axis is of the form (0, 0, z).

View the Topic in this video From 00:54 To 09:00

Disclaimer: Compete.etutor.co may from time to time provide links to third party Internet sites under their respective fair use policy and it may from time to time provide materials from such third parties on this website. These third party sites and any third party materials are provided for viewers convenience and for non-commercial educational purpose only. Compete does not operate or control in any respect any information, products or services available on these third party sites. Compete.etutor.co makes no representations whatsoever concerning the content of these sites and the fact that compete.etutor.co has provided a link to such sites is NOT an endorsement, authorization, sponsorship, or affiliation by compete.etutor.co with respect to such sites, its services, the products displayed, its owners, or its providers.

  • The co-ordinates of midpoint is \tt \left(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2},\frac{z_{1}+z_{2}}{2}\right)
  • The co-ordinates of centroid is \tt \left(\frac{x_{1}+x_{2}+x_{3}}{3},\frac{y_{1}+y_{2}+y_{3}}{3},\frac{z_{1}+z_{2}+z_{3}}{3}\right)