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Introduction

QUICK LINKS


Introduction

Translations

A translation is a type of rigid transformation, which means it changes the position or orientation of an image without changing its size or shape.

Just like how we have up/down and left/right buttons to control the movement of a video game character, we can use translations to control the movement of an image:
Enter the translation that takes us from our starting point to the blue, ending point:
Translation:
A translation is a set of directions in the form of a point
or a description ( units right/left and units up/down) that tells us how to move an image or shape.
Adding the translation to each original point of the image gives us the new points of the image.
Check out our step-by-step translations calculator to practice translating images or keep scrolling to learn more about how to do horizontal and/or vertical translations on a graph.

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Translations Calculator

Step 1. Identify the translation.

How is the translation described?

Step 2. Turn the description of the translation into a point.

DescriptionValue
right
up
right and up

Step 3. Identify the original points.

How many points does your shape have?

Step 4. Add the translation to the original points to get the new points.

Original PointTranslationNew Point

Step 5. Plot the new points and connect the dots.

Key Steps 🗝 How to Do Translations

Step 1. Identify the translation.

How is the translation described?

Step 2. Turn the description of the translation into a point.

DescriptionPoint
right
left
up
down
right, up
right, down
left, up
left, down

Step 2. Identify the original points.

Step 3. Add the translation to the original points to get the new points.

Original PointTranslationNew Point
...............

Step 4. Plot the new points and connect the dots.

Let’s check out some example problems of horizontal and vertical translations!

Translations

A translation works just like the up/down and left/right arrows we use to control the movement of a character of a video game.A translation is a set of directions for how to move an image and can be in the form of a point or a description ( units up/down and units right/left).
If and ,the translation is both horizontal and vertical.
Adding the translation to each original point of the shape gives us the new points of the shape.
Let’s walk through some examples to see this in action!
Let's start by translating this image :

Step 1. Identify the translation.

The translation is , which means we're translating right and up.

Step 2. Turn the description of the translation into a point.

DescriptionValue
right
up
right and up

Step 2. Identify the original points.

Original
Point 1
Point 2
Point 3
From the diagram, we can see that our original points are: .

Step 3. Add the translation to the original points to get the new points.

Original PointTranslationNew Point

Step 4. Plot the new points and connect the dots.

Nice work! Now let's try translating this image to the left and down:

Step 1. Identify the translation.

The translation is left and down.
↔️units↕️units

Step 2. Turn the description of the translation into a point.

DescriptionValue
left
down
left and down

Step 3. Identify the original points.

Original
Point 1
Point 2
Point 3
Point 4
From the diagram, we can see that our original points are: .

Step 4. Add the translation to the original points to get the new points.

Original PointTranslationNew Point

Step 5. Plot the new points and connect the dots.

If you’d like additional practice with translations, take a moment to complete the quick practice below before closing out this lesson! ⚡

Practice: Translations

Question 1 of 10: Translate the following figure by :

Step 1. Identify the translation.

Step 2. Turn the description of the translation into a point.

right and up

Step 2. Identify the original points.

Enter the original points of the shape:
Original Points
Point 1
Point 2
Point 3
Point 4

Step 3. Add the translation to the original points to get the new points.

Original Points+Translation=New Point
+=
+=
+=
+=

Step 4. Plot the new points and connect the dots.

Awesome job! Our new translated shape is the blue shape:

When you feel like you've mastered this lesson, click for a celebration ⬇️!
Nice work, look at you go! Thanks for checking out this lesson ☺️🙏. Where to next?