What is a Cartesian grid?

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

How do you find x and y coordinates?

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

Which comes first, x or y?

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

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Chapter overview

Learning goals

Maths

X and Y coordinates

Your lesson progress

Summary

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$x$ 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:

Maths; Straight line graphs; KS3 Year 7; X and Y coordinates

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.

$x$ 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: 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.

Frequently Asked Questions (FAQ)

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

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X and Y coordinates

​xxx​ and yyy​ coordinates

In a nutshell

The coordinate grid

Definition

Coordinates

​​procedure​

Example

Plotting coordinates

​​PROCEDURE​

​xxx​ and yyy​ coordinates

In a nutshell

The coordinate grid

Definition

Coordinates

​​procedure​

Example

Plotting coordinates

​​PROCEDURE​

Now you’ve read the summary, have a go at the exercises!

$x$ and $y$ coordinates

procedure

PROCEDURE

$x$ and $y$ coordinates

procedure

PROCEDURE