The Cartesian coordinate system allows ordered pairs to be displayed graphically.

Cartesian Coordinate System
a system for representing points on a plane in relation to a horizontal x-axis and a vertical y-axis whose point of intersection is labelled (0,0). This point of intersection is referred to as the origin.

Four points are plotted on the Cartesian coordinate plane below.

Using the Cartesian coordinate plane:

  • The horizontal and vertical axes should be labelled. Most commonly (but not always), the horizontal axis is labelled the x-axis and the vertical axis is labelled the y-axis.

  • Quadrants are named in a counter-clockwise direction, beginning with Quadrant I in the top right quadrant.

  • Titles are typically only used when a specific situation is being represented.

  • The origin can be used to locate or plot an ordered pair.

  • To plot an ordered pair that has a positive x and a positive y coordinate, start from the origin and move horizontally to the right and then vertically upwards according to the given coordinates.

    • To locate the ordered pair (1,3), move from the origin 1 unit to the right and 3 units up.

  • To plot an ordered pair that has a negative x and a positive y coordinate, start from the origin and move horizontally to the left and then vertically upwards according to the given coordinates.

    • To locate the ordered pair (−4,1), move from the origin 4 units to the left and 1 unit up.

  • To plot an ordered pair that has a negative x and a negative y coordinate, start from the origin and move horizontally to the left and then vertically downwards according to the given coordinates.

    • To locate the ordered pair (−2,−1), move from the origin 2 units to the left and 1 unit down.

  • To plot an ordered pair that has a positive x and a negative y coordinate, start from the origin and move horizontally to the right and then vertically downwards according to the given coordinates.

    • To locate the ordered pair (2,−2), move from the origin 2 units to the right and 2 units down.


Example 2

Plot the following points on the Cartesian coordinate plane provided.

{(−6,4), (−4,−3), (−2,0), (0,3), (0,−5), (3,6), (5,−4), (6,0)}

(−6,4): from (0,0), move 6 units to the left and 4 units up.

(−4,−3): from (0,0), move 4 units to the left and 3 units down.

(−2,0): from (0,0), move 2 units to the left and no movement up or down. This point lies on the x-axis.

(0,3): from (0,0), no movement left or right and movement 3 units up. This point lies on the y-axis.

(0,−5): from (0,0), no movement left or right and movement 5 units down. This point lies on the y-axis.

(3,6): from (0,0), move 3 units to the right and 6 units up.

(5,−4): from (0,0), move 5 units to the right and 4 units down.

(6,0): from (0,0), move 6 units to the right and no movement up or down. This point lies on the x-axis.