who proposed the coordinate system to describe the position of a point in a plane accurately

The coordinate system to describe the position of a point in a plane accurately is attributed to René Descartes. This system is often called the Cartesian coordinate system in his honor.

It's important to note that there were earlier ideas related to using coordinates. For instance, the concept of latitude and longitude for geographical locations predates Descartes. However, Descartes' system with perpendicular axes at the origin and using algebraic notation for coordinates is what revolutionized how we represent points on a plane.