Chapter overview Maths

Types of numbers

Number calculations

Fractions, decimals and percentages

Algebraic manipulation

Formulae and equations

Straight line graphs

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Ratio

Proportion

Rates of change

Shapes

Properties of shapes

Measures

Lines and angles

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Trigonometry

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Maths

# X and Y coordinates 0%

Summary

# ​$x$​ 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: The 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.

FAQs

• Question: What is a Cartesian grid?

Answer: The Cartesian grid is the same thing as the coordinate grid.

• Question: How do you find x and y coordinates?

Answer: Starting at the origin, go horizontally x places, given by the x-coordinate, then go y places vertically, given by the y-coordinate.

• Question: Which comes first, x or y?

Answer: When denoting coordinates, the x-coordinate comes before the y-coordinate: (x,y)

Theory

Exercises