What Are Cartesian Coordinates?

What Are Cartesian Coordinates?

Cartesian coordinates are used to describe the position of a point on a graph.

The image below shows a graph. A point is plotted on the graph (a blue cross) with its Cartesian coordinates written beside it: (2, 4).

Don't forget: a graph has a pair of axes: the horizontal axis is called the x-axis and the vertical axis is called the y-axis. They meet at the origin. We can plot points, lines and curves on a graph.

Interactive Widget

Use this interactive widget to generate Cartesian and polar co-ordinates. Simply click in the shaded area.





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How Do Cartesian Coordinates Work?

Cartesian coordinates work by measuring how far the point is from the origin.

  • First you measure how far across the point is (in the horizontal direction) by measuring how far along the x-axis it is. This is called the x-coordinate.

    The point above is 2 units along the x-axis so its x-coordinate is 2.

    Note: The x-axis is labelled with numbers (0, 1, 2, 3...) so you can measure how far across the point is.

  • Then you measure how far up the point is (in the vertical direction) by measuring how far up the y-axis it is. This is called the y-coordinate.

    The point above is 4 units along the y-axis so its y coordinate is 4.

    Note: The y-axis is labelled with numbers (0, 1, 2, 3...) so you can measure how far up the point is.

  • The x-coordinate (2) and the y-coordinate (4) are then written in brackets, separated by a comma. The x-coordinate is on the left, the y-coordinate is on the right.

Cartesian Coordinates in General

In general, we write Cartesian coordinates as:

x is the x-coordinate.

y is the y-coordinate.

x and y can taken any number (whole or fraction, positive or negative).

See Also

What are the parts of a graph? What is the x-axis? What is the y-axis? What is the origin?