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Cartesian Coordinates

Cartesian coordinates can be used to pinpoint where you are on a map or graph

(Play with the Interactive Cartesian Coordinates to see for yourself)

Cartesian Coordinates

Using Cartesian Coordinates you mark a point on a graph by how far along and how far up it is:

The point (12,5) is 12 units along, and 5 units up.

X and Y Axis

The left-right (horizontal) direction is commonly called X ...

... and the up-down (vertical) direction is commonly called Y.

The reference line (from which distances are measured) is called an Axis.

There is an X Axis and a Y Axis.

(The plural of Axis is Axes, and is pronounced ax-eez)

  The X Axis runs horizontally through zero
The Y Axis runs vertically through zero


As x (the first coordinate) increases, the point moves further right. (If it decreases, then the point moves further to the left.)
As y (the second coordinate) increases, the point moves further up. (If it decreases, then the point moves further down.)

Writing Coordinates

The coordinates are always written in a certain order: the horizontal direction first, then the vertical direction. This is called an "ordered pair".

And usually the numbers are separared by a comma, and parentheses are put around the whole thing like this: (3,2)

Example: (4,9) means 4 units to the right, and 9 units up

Example: (0,5) means 0 units to the right, and 5 units up. In other words, only 5 units up.

They are called Cartesian because the idea was developed by the mathematician and philosopher Rene Descartes who was also known as Cartesius. He is also famous for saying "I think, therefore I am".


What happens when x or y are negative? Well, start at zero and just head in the opposite direction!

This means it is possible to have combinations like positive x and negative y, or both x and y being negative. In fact there are 4 such combinations, and on the graph they are called Quadrants:

Example Quadrant
Positive Positive (3,2) I
Negative Positive (-4,3) II
Negative Negative (-2,-1) III
Positive Negative (2,-3) IV

The word Quadrant comes form quad meaning four. For example, four babies born at one birth are called quadruplets, and a four-legged animal is a quadruped)

Here are the four Quadrants shown on a graph:

Example: The point "A" (3,2) is 3 units along, and 2 units up. Both x and y are positive, so that point is in "Quadrant I"

Example: The point "C" (-2,-1) is 2 units along in the negative
direction, and 1 unit down (ie negative direction). Both x and y are negative, so that point is in "Quadrant III"

The Origin

The point (0,0) is given the special name "The Origin", and is sometimes given the letter "O".

Dimensions: 1, 2, 3 and more ...

Think about this:

1 The Number Line can only go left-right, so any position needs just one number
2 Cartesian coordinates can go left-right and up-down, so any position needs two numbers
3 How do we locate a spot in the real world (such as the tip of your nose)? We need to specify left-right, up-down, and forward-backward, that is three numbers, or 3 dimensions!


And Cartesian coordinates can be used for locating points in 3 dimensions as in this example:

Here the point (-4,-4,5) is shown in three-dimensional cartesian coordinates.

In fact, this idea can be continued into four dimensions and more - I just can't work out how to illustrate that for you!