Coordinate geometry is the study of geometric objects by assigning coordinates to points and translating geometric relations into algebraic equations. It is also called analytic geometry and, in the common Cartesian setting, Cartesian geometry.
In the plane with Cartesian coordinates, a point is represented by an ordered pair 
, while curves are represented by equations in 
and 
. Algebraic operations on these equations can be used to determine
intersections, distances, and tangencies. Other coordinate
systems may be chosen to match the symmetry of a problem, and coordinate transformations
express the same geometric object in different systems.
