Coordinate Geometry
Eucledean Geometry uses Propositions, Theorems and Properties to establish geometrical facts in a logical manner. The French Mathematician and Philosopher Rene Descartes was successful in using Algebraic techniques in solving Geometrical Problems. This blending of Algebra and Geometry had branched out as a subject in Mathematics known as Coordinate Geometry.
It is also commonly known as Analytical Geometry implying its algebraic empowerment. The coordinate system consisting of intersecting perpendicular lines at a point called Origin. The intersecting mutually perpendicular lines which determined the plane or space are called the axes of the Coordinate System.


In 2D Coordinate System the two axes X and Y intersect at the Origin O. A point is represented by an ordered pair (x, y). x represents the distance of the point measured horizontally while y the distance measured in the vertical direction. The origin O is represented by the ordered pair (0, 0). 
3D Coordinate System consists of mutually perpendicular axes X, Y and Z. A point is represented by an ordered triplet (x, y, z) each representing the distance measured along the corresponding axes. 