Analytical Geometry is a branch of mathematics that uses algebraic methods to study geometric shapes and their properties. It combines algebra and geometry by representing points, lines, and curves in a coordinate system, typically the Cartesian Coordinate System. This allows for the use of equations to describe geometric figures, making it easier to analyze their relationships and characteristics. In Analytical Geometry, each point in a plane is represented by a pair of numerical coordinates, usually written as (x, y). This framework enables the calculation of distances, midpoints, and slopes, as well as the ability to derive equations for lines and curves. It serves as a foundation for more advanced topics in mathematics and physics.