The Cartesian coordinate system is commonly used when drawing the graphs of functions and equations in Math.

It is sometimes referred to a the rectangular coordinate system, and is quite straight forward to understand.

This page will show some Cartesian coordinate system examples of how to plot points and draw graphs or shapes.

### Cartesian Plane:

Before looking at more specific Cartesian coordinate system examples, we need to have a clear understanding of what the Cartesian plane is.

There are 2 axis on the plane, a vertical

*axis, and a horizontal*

**y***axis, this pair of axes create 4 different quadrants in the Cartesian plane.*

**x**As can be seen, both the

*and*

**x***axis go in a positive and a negative direction, from the centre point.*

**y**The centre point of the axes is often referred to as the origin.

A coordinate on the Cartesian plane will have an

*x*value and a

*y*value together, written in brackets, (

*,*

**x***).*

**y**So the coordinates of the origin are (0,0).

The quadrants themselves also have specific numbers to represent them. Starting at the top right with 1, and then moving anti-clockwise to 4 in the lower right.

## Cartesian Coordinates

As mentioned, a point on the Cartesian plane will have a coordinate (

*,*

**x***).*

**y**We can see how this works with a random point, let’s say

**B (2,3)**.

As the coordinate is in the form (

*,*

**x***), for B we go 2 places along the*

**y***x*-axis, then 3 places up the

*y*-axis.

Coordinates can have negative values for the

*and*

**x***values also, with points possibly being in any of the 4 quadrants.*

**y**

__Example__

*(1.1)*Plot and draw a triangle on the Cartesian plane that has vertices at coordinates

**A(-2,-1)**,

**B(1,4)**and

**C(3,-2)**.

*Solution*For Cartesian coordinate system examples such as this, the approach is to plot the relevant points, then connect them up to form the correct shape.

## Cartesian Coordinate System Examples,<br>3D Cartesian Plane

We can also have a Cartesian plane in three dimensions or 3D.

For such Cartesian coordinate system examples, a

*axis is introduced and included with the*

**z***and*

**x***axis.*

**y**A point or coordinate in the 3D axis would be of the form

**(**.

*x,y,z*)The

*and*

**x***axis are still vertical and horizontal respectively, but the*

**y***axis means we can move a point closer to us, or further away.*

**z**We’ll draw a three dimensional cuboid in a 3D Cartesian axis below, to try and show how things work.

Understanding a 3D axis is particularly important when it comes to the topic of vectors.

__Example__

*(2.1)*On a 3D Cartesian axis draw a three dimensional cuboid with the following 8 vertices.

**a(1,0,0)**,

**b(4,0,0)**,

**c(1,0,2)**,

**d(4,0,2)**,

**e(1,3,0)**,

**f(4,3,0)**,

**g(1,3,2)**,

**h(4,3,2)**

*Solution*The approach is the same as with a 2D axis, plot the relevant vertices then join them up to form the shape.

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