Co-ordinates

 

Cartesian axes

This grid method of describing direction and position is the work of the Seventeenth Century French Philosopher and Mathematician René Descartes.

The x axis goes along horizontally.
The y axis goes vertically upwards.
They cross at the Origin,  O.

Co-ordinates are written inside brackets, with a comma separating the x and y values. The x value comes before the y value.

 

Any point plotted to the right of the zero will have a positive x co-ordinate.

Any point plotted above the zero will have a positive y co-ordinate.

Sometimes, only the positive quadrant is shown:

To read Cartesian co-ordinates:-

• Start at zero
• Count the number of units along or back.  This gives the x co-ordinate.
• Count the number of units up or down.  This gives the y co-ordinate.
• write down your numbers inside brackets, with a comma.

Example

A is the point ( 3, 2)
it is 3 units along, and 2 units up.

B is the point ( -2, -1)
it is 2 units back, and 1 unit down.

C is the point ( -4, 3)
it is 4 units back, and 3 units up.

 

   To plot Cartesian co-ordinates:-

• Start at zero
• Count the number of units along or back.  This gives the x co-ordinate.
• Count the number of units up or down.  This gives the y co-ordinate.
• Put  a dot and label.

 

Examples

Plot the point G (3, -2)

 

G is 3 units to the right and 2 units down.

 

Remember
x along, y to the sky.
Wise up   ( y is up )
Along the corridor, then up the stairs

 

3D Co-ordinates

With 3D co-ordinates, the x axis runs from left to right, the y axis runs in and out of the page, the z axis runs up and down.

 

 

This time, 3 figures are given, ( x, y, z)

So (3,2,1) is

 

 

Polar Co-ordinates

Each point is uniquely identified by a length and an angle.
 Polar co-ordinates are usually of the form ( radius, θ), where θ is measured anticlockwise from the x axis in degrees or radians.

Because it is a length, the first co-ordinate is positive.

Examples

A has co-ordinates (2,45° ) which means it has length 2 units and is angled at 45° .

B has co-ordinates (4,156° ) which means it has length 4 units and is angled at 156°

 

Notice that this is the same as the CAST diagram for trigonometry!