Concept of Coordinate Geometry

 

Concept of Coordinate Geometry

At its heart, coordinate geometry is a branch of mathematics that bridges the gap between algebra and geometry. It provides a systematic way to describe the position of points, lines, curves, and other geometric shapes using numbers, known as coordinates. Imagine it as a universal addressing system for the geometric world.  

The foundation of coordinate geometry lies in the Cartesian coordinate system, named after the French mathematician René Descartes. This system uses perpendicular lines, called axes, to define a plane.  

• Axes: Typically, we have a horizontal axis called the x-axis and a vertical axis called the y-axis. These axes intersect at a point called the origin, which represents the zero point for both axes. In three-dimensional space, a third axis, the z-axis, is introduced, perpendicular to both the x and y axes.  

• Coordinates: The position of any point in this system is uniquely defined by an ordered pair (in 2D) or an ordered triplet (in 3D) of numbers, called its coordinates. For a point P in 2D, its coordinates are represented as (x,y), where x is the perpendicular distance from the y-axis (the abscissa) and y is the perpendicular distance from the x-axis (the ordinate). Similarly, in 3D, a point's coordinates are (x,y,z).