Cartesian Coordinate System

The Cartesian coordinate system is a mathematical concept that uses two perpendicular axes to specify the position of points in a plane or space. Named after the French mathematician and philosopher René Descartes, it provides a systematic way to describe geometric figures and their relationships algebraically.

The horizontal line is called the “x-axis”. From the left, it is the negative x-axis, and on the right is the positive x-axis

The vertical line is the “y-axis”. From the bottom it is the negative y-axis and from the top it is the positive y-axis

Where the two lines meet in the middle is called the Origin and separates positive from negative

The squares contained by the axis are called quadrants

Ordered Pairs

Ordered pairs are the way we describe the location on the Cartesian Plane. Depending on the quadrant, x and y will be positive or negative. For example, in quadrant 1, the x value will always be positive and y will always be positive because they are located on the positive x-axis and positive y-axis

The Origin will have the coordinates (0,0) meaning that it is located 0 on the x axis and 0 on the y-axis

The x coordinate will ALWAYS be listed first!

For Example in the coordinate plane below

Point A has the ordered pair (6,7) because you move over 6 on the x axis and up 7 on the y axis and both are positive since it is in quadrant 1

Point B has the ordered pair (-5, -2) because you move over 5 on the negative x axis and down 2 on the y axis. Both are negative since it lies in quadrant 3