# Translations on a grid

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## What are translations on a grid?

Before we look at translations on a grid, we need to know what a 2d grid with coordinates is. It is made up of an x axis which goes across and a y axis which goes up and down. These meet at the origin which is marked by zero. A translation is when we make a movement on a grid. We can move individual points or entire shapes. Here we will just focus on translating individual points or coordinates.

## How do we make a translation?

When we make translations on a grid, we always move in steps. First we go across, left or right, then we go up or down. We move along the x axis first and up or down the y axis second. To identify the translations that you need to make, identify where you are starting, then look at when you are going to end up.

## Step by step translations

Step 1. Identify where you are starting. Step 2. Look where you want to end up. Step 3. Look along the x axis and decide whether you need to move left or right Step 4. How many steps or squares do you need to make along the x axis? Step 5. Do you need to move up or down the y axis? Step 6. Count how many steps up or down you need to move on the y axis. Step 7. You can now make the translation along the x axis and up or down the y axis.

## How do we describe translations?

We can talk about a translation as a movement and say that we moved a certain number or steps left or right along the x, and a certain number or steps up or down the y. For example, they moved 3 right and 2 down. This would be x + 3, y -2.

## More practise

For more practise on translating coordinates or making translations on a grid, try the worksheets or exercises that can be found on this site.

### TranscriptTranslations on a grid

"It’s such a nice day- shall we go out and get some ice cream?" "Sure- we could go in our new robot car. But just one thing, can we go and pick up my Granny on the way? She loves ice-cream!" "Er, Nico, do you know the way to your Granny’s house?" "Errrr?" Let’s help Nico and Nia to travel by learning about: ‘Translations on a grid’. On every coordinate grid there are two axes. The x axis, which goes across and the y axis, which runs up and down. These meet at the origin, which is marked by a zero. When we make a movement on a grid we call it a translation. When we make a translation, we always move across first, and up or down second. Here is a coordinate grid for a map of the town. Nico and Nia are here and Nico’s Granny is here. How will they get to Nico’s Granny’s house? They will need to go across to here, then down to here. First they need to go across; do they need to go left or right? Right. How many squares right do they need to travel? Three. Next, do they need to travel up or down? Then they need to travel down; how many squares down do they need to go down by? They need to move two squares down. "It looks like Granny's not in. Let's programme the car to go to the park." Nico and Nia are at Granny's house which is here and they want to get to the park which is here. How will Nico and Nia get from Granny's house to the park? First they need to move across the x axis. Should they go left or right? They should go right. How many squares to the right should they travel? They should travel two squares to the right. Then they need to move along the y axis, should they go up or down? They need to go up. How many squares should they go up by? They should go up by two squares. "Hey Granny- jump in, we're going for ice cream!" Let's look at the map to work out how to get from the park to the ice-cream van. How will they get from the park here, to the ice cream van here? What is the translation they need to make? They need to go left five and down three. "I can see the ice cream van!" Before they all enjoy some ice cream, remember: A coordinate grid is made up of two axes. An x axis and a y axis, which meet at the origin. When we make movements on a grid we call it a translation. We always move across the x axis first, and up or down the y axis second. We can then say how many units we moved left or right and up or down. "Oh no! They're all sold out!" "Oh no. It's a good job I stocked up my freezer with ice-creams last week!"

## Translations on a grid exercise

Would you like to apply the knowledge you’ve learnt? You can review and practice it with the tasks for the video Translations on a grid .
• ### What are the names of each axis?

Hints

The x axis is horizontal and runs across.

The y axis is vertical and runs up and down.

The axes are straight lines.

Solution

The x axis is horizontal and runs across from left to right, and is shown here in yellow.

The y axis is vertical, it runs up and down and is shown here in green.

• ### How do we make a translation?

Hints

Before we move or make a translation, we need to identify where we are starting.

Remember, we always go along the x axis before we move up or down the y axis.

We move up or down the y axis after we have moved along the x axis.

Solution

These are the steps we need to follow to make a translation.

• ### How will they get to the boat?

Hints

Start at the black dot by the car and move to the black dot by the boat.

Remember that we always move along the x axis first. Do Nico and Nia need to go left or right?

How many units down do they need to move to reach the boat? Count carefully.

This arrow is pointing left.

Solution
• How will Nico and Nia get to the boat? First, they need to go along the x axis.
• They will need to move left 1 unit.
• Then they need to go down the y axis.
• Then they will need to move down 4 units.
• ### How will they get to the cafe?

Hints

They are starting at the boat which is at (1, 3), and they need to get to the cafe which is at (7, 8).

Remember, we always go along the x axis first and up or down the y axis second.

Solution
1. To get to the cafe, first they will need to move right.
2. They will need to move along 6 units.
3. Then they will need to move up.
4. They need to move up the y axis by 5 units.
• ### Where will they end up?

Hints

First, move Nico and Nia's car right 3 units.

Then, how many units do they need to move down?

Finally, where do they end up after making the movement across and down?

This arrow is pointing right.

Solution

If Nico and Nia made a translation of 3 units right and 4 units down, they would end up at the lighthouse!

• ### How will Nico and Nia get home?

Hints

They need to travel along the x axis first, so we need to go either left or right.

You need to translate the car to the house. First move along, then move up or down.

This direction is left.

Solution

To get from the car to the house, Nico and Nia need to move left 2 and down 3.