# $x$ and $y$ coordinates

## In a nutshell

Coordinates allow you to talk about location on a coordinate grid with precision. In $2\text{D},$ $x$ and $y$ coordinates are conventionally used and together are denoted as $(x,y)$.

## The coordinate grid

In $2\text{D},$ the coordinate grid (also known as the Cartesian grid) consists of an $x$-axis going horizontally and a $y$-axis going vertically:

### Definition

The "origin" is the centre of the coordinate grid. When reading and plotting coordinates, start from the origin.

## Coordinates

#### procedure

1. | To describe a point on the coordinate grid, read along the $x$-direction first (left or right) and find the number the point is in-line with. This number is the $x$-coordinate. |

2. | Then read along the $y$-direction (up or down). The number that the point is in-line with is the $y$-coordinate. |

3. | The coordinates are then written in the form $(x,y)$ where $x$ is the $x$-coordinate, and $y$ is the $y$-coordinate. |

##### Example

*If you have the point *$(5,8)$* on the coordinate grid, it would be in-line with the *$5$* on the $x$-axis and in-line with the $8$ on the $y$-axis, as shown below:*

**Note:** *Coordinates ***must** be given with the $x$-coordinate first and the $y$-coordinate second. If you reverse these numbers, you end up with a different point! For example, if you look at $(8,5)$*, you actually have the point depicted below:*

**Note:** T*he origin has coordinates *$(0,0)$*.*

## Plotting coordinates

#### PROCEDURE

1. | To plot a point on the coordinate grid, read the coordinates, which are in the form $(x,y)$. Read along the $x$-direction first (left or right) by the number given by $x$. If $x$ is positive, you go to the right of the origin, and if it is negative, you go left. |

2. | Then go along the $y$-direction (up or down) by the number given by $y$. If $y$ is positive, go up, and if it is negative, go down. |

3. | Mark the point on your coordinate grid. It is common to use a dot or a cross. |