What is the cartesian coordinate system?

he Cartesian coordinate system is a fundamental framework in mathematics and physics used to specify the position of points in space. It is named after the French mathematician and philosopher René Descartes, who introduced the concept in the 17th century. The system uses perpendicular axes to define the coordinates of points, making it a cornerstone of geometry, algebra, and many scientific fields.

Components of the Cartesian Coordinate System

1. Axes

   • In 2D, the system consists of two perpendicular axes:
     • x-axis (horizontal)
     • y-axis (vertical)
   • In 3D, there is an additional axis:
     • z-axis (depth)

     • Origin (0,0) or (0,0,0)

       • The point where all axes intersect is called the origin.
       • It is denoted as (0,0) in 2D and (0,0,0) in 3D.

     • Coordinates (x, y, z)

       • A point is represented as an ordered pair (x, y) in 2D or an ordered triplet (x, y, z) in 3D.
       • The values of x, y, and z specify the position of the point relative to the origin.

Quadrants in 2D Cartesian Plane

The 2D Cartesian plane is divided into four quadrants, based on the signs of

$x$

x and

$y$

y:

Applications of Cartesian Coordinates

• Geometry (defining shapes and graphs)
• Physics (describing motion and forces)
• Engineering & Robotics (positioning objects)
• Computer Graphics (3D modeling and animations)
• Navigation & GPS (mapping locations)

What is the cartesian coordinate system?

https://www.youtube.com/watch?v=TJ3WSTu8isY