Who developed the idea of coordinate geometry?

Answer 1

Coordinate geometry is also called Cartesian geometry (as in Cartesian coordinates). The word "Cartesian" comes from "Descartes". It was René Descartes, the French mathematician and philosopher who merged algebra and geometry & so laid the foundations to coordinate geometry.

Answer 2

As in Cartesian Coordinates?
"The idea of this system was developed in 1637 in two writings by Descartes." http://en.wikipedia.org/wiki/Cartesian_coordinate_system
or polar coordinates
http://en.wikipedia.org/wiki/Polar_coordinates#History