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).

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  • 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)