# What Are Cartesian Co-ordinates? (Mathematics Lesson)

# What Are Cartesian Co-ordinates?

Cartesian co-ordinates can be used to describe a point on a graph.Cartesian co-ordinates are described by a pair of numbers in a bracket, separated by a comma.

- The number on the left gives the
**x co-ordinate**: how far the point is along the x-axis. - The number on the right gives the
**y co-ordinate**: how far the point is up the y-axis.

# How to Describe a Point in Cartesian Co-ordinates

**Question**: What are the Cartesian co-ordinates of the point shown on the graph below?

Step 1

**straight down**from the point to the x-axis.

Read off the x value. This is the

**x co-ordinate**.

The x co-ordinate is 3.

Step 2

**straight across**from the point to the y-axis.

Read off the y value. This is the

**y co-ordinate**.

The y co-ordinate is 4.

Step 3

**( x co-ordinate , y co-ordinate )**

The co-ordinate is

**(3,4)**.

# How to Draw a Point in Cartesian Co-ordinates

**Question**: Draw the point described by the Cartesian co-ordinates (2,5) on a graph.

Step 1

The x co-ordinate is 2.

Step 2

**straight up**from the x-axis at the value of the x co-ordinate.

Step 3

The y co-ordinate is 4.

Step 4

**straight across**from y-axis at the value of the y co-ordinate.

Step 5

##### Quick Test

**show**

##### Note

**WHAT'S IN A NAME?**

Cartesian co-ordinates 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!

He also developed the use of superscript to denote powers:

**x**,

^{2}**y**.

^{4}# FOUR QUADRANTS

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

**DON'T MIX UP THE CO-ORDINATES**

An easy mistake to make is to mix up the x and y co-ordinates.

- The co-ordinate on the left is the x co-ordinate.

It describes how far along the x-axis, or how far across, the point is. - The co-ordinate on the right is the y co-ordinate.

It describes how far up the y-axis, or how far up, the point is.