Coordinate geometry, also known as analytic geometry, is a branch of mathematics that involves the study of geometric shapes using algebraic equations. It is a powerful tool that enables mathematicians to quantify geometric properties and describe them in terms of coordinates. There are various synonyms to coordinate geometry, including analytical geometry, Cartesian geometry, and coordinate mathematics. Analytical geometry refers to the study of geometrical objects using mathematical equations, while Cartesian geometry is named after Rene Descartes, who developed the Cartesian coordinate system. Coordinate mathematics is a broad term used to describe the mathematical applications that utilize coordinates, including vectors, matrices, and graphs. Ultimately, each of these terms refers to the same fundamental concept of using algebraic equations to study geometric shapes.