## The Lesson

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.

## 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).

## What's in a Name?

Cartesian coordinates are named after the French philospher, mathematician and writer, RenĂ© Descartes. Descartes is famous for the phrase "*Cogito ergo sum*" - 'I think therefore I am'. In mathematics, Descartes laid down many of the conventions on notation we use today. In algebra, he was the first to call unknowns

**x**,

**y**and

**z**, and knowns

**a**,

**b**and

**c**. If you still get confused having letters stand in for numbers, blame Descartes!

## Four Quadrants

x-coordinates and y-coordinates can be positive and negative. This means there are four quadrants made by the two axes.## Beware

## Don't Mix Up The Coordinates

An easy mistake to make is to mix up the x and y coordinates.-
The coordinate on the left is the x-coordinate.
It describes how far along the x-axis, or how far across, the point is.
Remember,
**x is a cross**! - The coordinate on the right is the y-coordinate. It describes how far up the y-axis, or how far up, the point is.