Introduction to Coordinate Geometry

In coordinate geometry, the measurements are done with respect to spacial reference frames. These reference frames are known as Coordinate Systems. Any coordinate system is generally chosen depending on the kind of geometric objects that need to be measured/represented or the kind of measurements that need to be done. This is because some coordinate systems are much more suitable/intutive/easier for certain geometric measurements/representations than others. The coordinate systems that are generally used are the following:

  1. 2D: Cartesian, Polar
  2. 3D: Cartesian, Spherical, Cylindrical
All the coordinate systems mentioned above are orthogonal coordinate systems.

Geometric objects are represented mathematically through equations. These equations can have different representations depending on the following:
  1. The coordinate system that is used.
  2. The actual form in which equations are represented.
Following are the different forms in which equations can be represented in any coordinate system
  1. Scalar form: The equation is given in form of some function of coordinates of the coordinate system.
  2. Parametric form: The equation are given in form of equations of coordinates of the coordinate system which are themselves specified in terms of 1 or more parameters.
  3. Vector form: The equation is given for position vector of all points of geometric object. The components of this vector are themselves specified using parametric representation of the coordinates and the basis vectors of coordinate system.