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What Is a Co-ordinate? (Mathematics Lesson)

What Is a Co-ordinate?

A co-ordinate describes a point on a graph.

There are different types of co-ordinate system.

Cartesian Co-ordinates

The most common type of co-ordinate system is Cartesian co-ordinates.

Cartesian co-ordinates tell you how far along and how far up a point is.

  • How far along is measured by the distance of the point along the x-axis.

  • How far up is measured by the distance along the y-axis.

How to Describe Cartesian Co-ordinates

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.
Question: Where is the point (2,4) on a graph?



On the graph below, the point is 2 along the x-axis and 4 up the y-axis.

Read more about Cartesian co-ordinates.

Polar Co-ordinates

Another type of co-ordinate system is polar co-ordinates.

Polar co-ordinates are useful for working with circular shapes.

Polar co-ordinates tell you how far from the origin a point is and the angle of the point from the horizontal axis.

How to Describe Polar Co-ordinates

Polar co-ordinates are described by a pair of numbers in a bracket, separated by a comma.



  • The number on the left gives the radial co-ordinate r: the length of the line segment joining the origin to the point.

  • The number on the right gives the angular co-ordinate θ: the angle between the line segment joining the origin to the point and the horizontal axis.
Question: Where is the point (5,45°) on a graph?



On the graph below, if a line segment is drawn from the origin to the point, the line is 5 long from the origin and 45° from the horizontal axis.



Read more about polar co-ordinates.
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.

CONVERTING BETWEEN CARTESIAN AND POLAR CO-ORDINATES

It is possible to convert between Cartesian and polar co-ordinates.



Using Pythagoras' Theorem and trigonometry, the relationship between x, y, r and θ can be found.



CO-ORDINATES IN 3D

The co-ordinate systems seen so far have been in 2D. They can be extended to 3 dimensions by adding a z-axis perpendicular to the graph plane.