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Chapter overview
Learning goals
Learning Goals
Maths
Types of numbers
Number calculations
Fractions, decimals and percentages
Algebraic manipulation
Formulae and equations
Straight line graphs
Other graphs
Ratio
Proportion
Rates of change
Shapes
Properties of shapes
Lines and angles
Drawing shapes
Trigonometry
Probability
Maths
Summary
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 $(x,y)$.
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:
The "origin" is the centre of the coordinate grid. When reading and plotting coordinates, start from the origin.
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. |
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 $(0,0)$.
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. |
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 $(x,y)$.
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:
The "origin" is the centre of the coordinate grid. When reading and plotting coordinates, start from the origin.
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. |
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 $(0,0)$.
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
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