## 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, René 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!

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