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-ordinatesThe 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-ordinatesCartesian 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.
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-ordinatesAnother 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-ordinatesPolar 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.
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.
NoteWHAT'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.