Definition

1. Noun:
   • A Cartesian coordinate is a number that specifies the location of a point along a specific axis in a Cartesian coordinate system. A single coordinate, such as 3 or -5.2, is not a complete location by itself. A complete position is described by an ordered set of these coordinates (e.g., (3, -2) in two dimensions, or (1, 5, -2) in three dimensions).
   • The system is defined by perpendicular reference lines (axes) that intersect at a common origin point. Distances from these axes are measured using these coordinates.

Examples of Usage

• Noun:
  • In the ordered pair (7, 4), the first Cartesian coordinate, 7, represents the point's distance along the x-axis.
  • To plot the point, you start at the origin and move according to each Cartesian coordinate in the ordered set.
  • The z-coordinate in a three-dimensional system indicates the point's position relative to the vertical plane.

Advanced Usage

• n-dimensional Cartesian coordinates: The concept extends beyond three-dimensional space to any number of dimensions (n) in mathematics and physics, where a point is defined by an ordered n-tuple of coordinates .
• Cartesian Coordinate System: The full framework consisting of the origin, perpendicular axes, and the rules for assigning coordinates to points. A single "Cartesian coordinate" is a component of this system.

Variants and Related Words

• Coordinate (n): The more general term for a value used to define a point's position within a system. "Cartesian coordinate" is a specific type of coordinate.
• Abscissa (n): A specific term for the x-coordinate (the first coordinate) in a two-dimensional Cartesian system.
• Ordinate (n): A specific term for the y-coordinate (the second coordinate) in a two-dimensional Cartesian system.
• Ordered Pair (n): A set of two numbers, like (x, y), that together give a complete location in two-dimensional Cartesian space.
• Ordered Triple (n): A set of three numbers, like (x, y, z), that together give a complete location in three-dimensional Cartesian space.

Synonyms

• Axis value
• Position value

Related Phrases

• Plot a point: To mark a location on a graph using its Cartesian coordinates.
  • The first step is to plot the point (2, -3) on the grid.
• Coordinate axes: The perpendicular reference lines (e.g., x-axis and y-axis) that define the system.
  • The point lies to the right of the origin because its x-coordinate is positive.

Noun

1. one of the coordinates in a system of coordinates that locates a point on a plane or in space by its distance from two lines or three planes respectively; the two lines or the intersections of the three planes are the coordinate axes