# What Are Cartesian Coordinates? (Mathematics Lesson)

# 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.

# 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).

# Using Cartesian Coordinates

Cartesian coordinates are used in many places.To use them, you must able to do two things:

- Draw a point on a graph when you are given its Cartesian coordinates.

Read more about how to draw a point from Cartesian coordinates - Read off the Cartesian coordinates of a point on a graph.

Read more about how to read off the Cartesian coordinates from a point

##### Interactive Test

**show**

Here's a second test on Cartesian coordinates.

Here's a third test on Cartesian coordinates.

##### Note

# 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!

# Four Quadrants

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.