Definition

1. Noun:
   • A Cartesian coordinate system is a coordinate system in which the position of a point is uniquely specified by its distances from a set of perpendicular lines (axes) that intersect at a common point called the origin.

Usage

• The Cartesian coordinate system is the fundamental system used in analytic geometry to describe geometric shapes with algebraic equations.
• In a two-dimensional Cartesian coordinate system, a point is defined by an ordered pair (x, y).
• Most common graphs, like line graphs and bar charts, are plotted using a Cartesian coordinate system.

Examples

• Noun:
  • The graph of the function y = 2x + 1 is drawn on a Cartesian coordinate system.
  • To find the distance between two points, you first plot them on a Cartesian coordinate system.
  • Physics problems often use a three-dimensional Cartesian coordinate system to describe motion in space.

Advanced Usage

• "n-dimensional Cartesian coordinate system": An extension of the system to spaces with more than three dimensions, where a point is defined by an ordered n-tuple (x₁, x₂, ..., xₙ).
  • Linear algebra frequently operates within an n-dimensional Cartesian coordinate system.

Variants and Related Words

• Cartesian coordinates (n.pl.): The set of numbers that locate a point in a Cartesian coordinate system (e.g., (3, -5) or (1, 2, 0)).
  • The Cartesian coordinates of the origin are (0,0).
• Cartesian plane (n.): The two-dimensional space formed by the x-axis and y-axis of a Cartesian coordinate system.
  • The parabola was sketched on the Cartesian plane.
• Rectangular coordinate system (n.): A synonym for Cartesian coordinate system, emphasizing the right angles between the axes.

Synonyms

• Rectangular coordinate system: A system using perpendicular axes.
• Coordinate grid: A network of lines used to locate points.

Related Concepts

• Origin: The point (0,0) in a 2D system, or (0,0,0) in 3D, where the axes intersect.
• Axes (singular: axis): The reference lines (usually labeled x, y, and z) that define the system.
• Ordered pair/triple: A pair or triple of numbers (like (x, y)) that gives the coordinates of a point.
• Quadrant: Any of the four regions into which the x- and y-axes divide the Cartesian plane.

Noun

1. a coordinate system for which the coordinates of a point are its distances from a set perpendicular lines that intersect at the origin of the system