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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
Draw a line (mentally or otherwise) 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
Draw a line (mentally or otherwise) 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
Write the Cartesian co-ordinates as
( 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
Find the x co-ordinate of the point.



The x co-ordinate is 2.

Step 2
Draw a line (mentally or otherwise) straight up from the x-axis at the value of the x co-ordinate.



Step 3
Find the y co-ordinate of the point.



The y co-ordinate is 4.

Step 4
Draw a line (mentally or otherwise) straight across from y-axis at the value of the y co-ordinate.



Step 5
The point described by the Cartesian co-ordinates is found at the intersection of the two lines.

Interactive Widget
Here is an interactive widget to help you learn about Cartesian and polar_coordinates.
Quick Test
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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: x2, y4.

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.