# Functional Skills: Coordinates

## Functional Skills: Coordinates Revision

**Coordinates**

We use **coordinates** to describe the positions of points on a grid in terms of their positions along the x-axis (horizontal) and y-axis (vertical).

There are **4** skills that you need to learn.

Make sure you are happy with the following topics before continuing.

**Skill 1: Understanding Coordinate Grids**

Points can be plotted and lines can be drawn on a grids similar to that seen.

A grid is made by 2 lines crossing called **axes**, meeting at a point in the middle called the **origin**.

The **x-axis** is the horizontal axis (left to right) and the **y-axis** is the vertical axis (bottom to top).

Coordinates are described by a pair of coordinates (\textcolor{red}{x}, \, \textcolor{blue}{y}) and represented by a dot or cross. The x coordinate is always written first.

The origin has coordinates (0, 0).

**Skill 2: Reading off Coordinates**

You may be asked to find the coordinates of a point on a grid.

**Example:** What are the coordinates of the point **A** on the grid?

For the x coordinate, go up from **A** to the x-axis. Read off the number:

\textcolor{red}{2}

For the y coordinate, go across from **A** to the y-axis. Read off the number:

\textcolor{blue}{-3}

So, the coordinates of **A** are:

(\textcolor{red}{2} , \, \textcolor{blue}{-3} )

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**Skill 3: Plotting Points**

You may also be asked to plot points on a grid, if you are given their coordinates.

**Example:** Plot the point (1, \, 3) on the grid.

Move right from the origin to find \textcolor{red}{1} on the x-axis.

Move up from 1 until you are level with \textcolor{blue}{3} on the y-axis.

Mark this position with a dot or a cross, and label it (\textcolor{red}{1}, \, \textcolor{blue}{3}).

**Skill 4: Plotting Lines and 2D Shapes**

You can connect points on a grid to **make lines or 2D shapes**.

e.g. the grid shows a triangle drawn by plotting 3 points and connecting them with straight lines.

We call the triangle ABC after the letters of its corners.

**Note:** You may be given dimensions in a question and have to use these to plot points and create 2D shapes.

**Example: Plotting Lines and 2D Shapes**

Using the grid, find the coordinates of **C** and **D** such that rectangle **ABCD** has an area of 15 cm^2.

Key: 1 \text{ square} = 1 \text{ cm}^2

**[2 marks]**

The distance between **A** and **B** is 5 cm.

If the area of the rectangle is 15 cm^2, then the shorter sides must be 15 \div 5 = 3 cm.

Since **ABCD** is a rectangle, points **C** and **D** must be directly below **A** and **B**. So, their y-coordinates will be 3 less than **A** and **B**.

Therefore, coordinates of point **C** will be (2,1) and the coordinates of point **D** will be (-3, 1).

## Functional Skills: Coordinates Example Questions

**Question 1:** What are the coordinates of the points A and B on the grid below?

**[2 marks]**

A is 3 left and 3 down, so A’s coordinates are (-3,-3)

B is 4 right and 1 up, so B’s coordinates are (4,1)

**Question 2:** Plot the point (-1,2) on the grid below.

**[1 mark]**

Move left from the origin to find -1 on the x-axis.

Then, move up from -1 until you are level with 2 on the y-axis.

Mark this position on the grid and label the point (-1,2).

**Question 3:Â **Points A and B have been plotted on the grid below.

Given that ABCD is a square, what are the coordinates of C and D?

Key: 1 \text{ square} = 1 \text{ cm}^2

**[2 marks]**

The distance between A and B is 4 cm.

ABCD is a square, so all sides must be 4 cm.

Also, C and D must be directly to the right of A and B. So, their x-coordinates will be 4 more than A and B.

Therefore, coordinates of point C will be (2,-1) and the coordinates of point D will be (2,3).

## Functional Skills: Coordinates Worksheet and Example Questions

### Coordinates L2

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