Cartesian Coordinate System Overview

Introduction to Cartesian Coordinate System

• The Cartesian Coordinate System is a method of locating points in space using an origin, x- and y-axes, and a unit length.
• According to legend, French mathematician Rene Descartes developed the system while observing a fly on the ceiling.

Cartesian Graph

• A Cartesian graph is composed of a horizontal line (x-axis) and a vertical line (y-axis) that intersect at the origin.
• The axes can be divided and numbered using any unit of measurement.
• Points are located on the graph using ordered pairs, where the first number is the x-coordinate and the second number is the y-coordinate.

Locating Points

• The x-coordinate indicates the distance from the y-axis along the x-axis, and the y-coordinate indicates the distance from the x-axis along the y-axis.
• Points can be located in one of four quadrants: I (above x-axis and to the right of y-axis), II (above x-axis and to the left of y-axis), III (below x-axis and to the left of y-axis), and IV (below x-axis and to the right of y-axis).
• Quadrant I has positive x- and y-coordinates, Quadrant II has negative x-coordinates and positive y-coordinates, Quadrant III has negative x- and y-coordinates, and Quadrant IV has positive x-coordinates and negative y-coordinates.

Three or More Dimensions

• The Cartesian Coordinate System can be extended to three dimensions by adding a z-axis, which begins at the origin and extends in positive and negative directions perpendicular to the coordinate plane.
• The z-axis allows for the indication of height or depth of a 3-dimensional figure.

Graphing Lines

• Lines can be graphed using Cartesian coordinates and equations, such as y = 2x, y = -3x -2, and y = 1/4x -2.
• Points on the graph can be located and connected to form a straight line.