Geometry » Coordinates

2D coordinates

Assenstelsel 2D

To the right you can see a coordinate system with a number of points. You always first read off the horizontal coordinate. In this case on the x-axis. Then you read off the vertical coordinate. In this case the y-axis. These two coordinates are always separate by a comma. So (x, y). If the point has a name (a capital letter) you write it immediately in front of the first bracket. Use no marks/signs between the capital letter and the first bracket.

The first five points in this coordinate system have the following coordinates:

A(2, 0) B(2, 4)C(5, 2)D(7, 0)E(0, 7)

Broken numbers:

If you have a point that is not on a grid point and the x-coordinate is therefore for example 1.5 make sure you make a legible difference between your decimal dot(s) and the comma.
You can also choose to write fractions instead of decimal numbers.
In countries where a decimal comma is used, the semicolon ( ; ) is used instead of the comma to separate the two coordinates.

The other two points in this coordinate system have the following coordinates:
Countries using a decimal dot:    
F(6.5, 5) or F(612, 5)
G(4.5, 6.5) or G(412, 612)
Countries using a decimal comma:
F(6,5; 5) or F(612, 5)
G(4,5; 6,5) of G(412, 612)

Note: The semicolon can always be used.
Even if there are no decimal numbers.

3D coordinates

On the right you see a drawing of a solid. A cube, to be precise.

Assenstelsel 3D

Just like you can use coordinates to indicate locations in a 2D coordinate system, you can also indicate points in space with a 3D coordinate system.

The only thing we need is another axis. This axis is called the z-axis. With this extra axis you have a xyz-system. See the drawing.

Indicating a point on the cube is done in almost the same way as in a 2D coordinate system. The coordinates are between brackets and separated by a comma ( , , ) or a semicolon ( ; ; ).
The coordinates are written in this order: (x , y , z).

Example

E(4, 0, 4)
You first go 4 steps towards the front, always starting in the origin. That is the x-coordinate. You are in point A then. Next you are going 0 steps towards the right, that is the y-axis. So you stay in point A. Finally you go 4 steps upwards, that is the z-axis. You arrived in point E.