What is Translation in Math? - Definition, Examples, & Terms

An error occurred trying to load this video.

Try refreshing the page, or contact customer support.

Coming up next: Fixed Interval: Examples & Definition

You're on a roll. Keep up the good work!

Take Quiz Watch Next Lesson
Your next lesson will play in 10 seconds
  • 0:03 Translation Definition
  • 0:53 How to Perform Translations
  • 2:37 Examples
  • 3:59 Lesson Summary
Save Save Save

Want to watch this again later?

Log in or sign up to add this lesson to a Custom Course.

Log in or Sign up

Speed Speed

Recommended Lessons and Courses for You

Lesson Transcript
Instructor: Jennifer Beddoe

Jennifer has an MS in Chemistry and a BS in Biological Sciences.

In mathematics, translation refers to moving an object without changing it in any other way. This lesson will describe how to translate an object and give some examples. A quiz will follow to test your knowledge.

Translation Definition

Translation is a term used in geometry to describe a function that moves an object a certain distance. The object is not altered in any other way. It is not rotated, reflected or re-sized.

The rust-colored item is the pre-image, and the blue item is the image.

In a translation, every point of the object must be moved in the same direction and for the same distance.

When you are performing a translation, the initial object is called the pre-image, and the object after the translation is called the image. So, in the picture above, the rust-colored item is the pre-image, and the blue item is the image. We know this because the arrow tells us the direction in which the image was moved. For other images, you might be told which image is the pre-image, or you might be asked to find either the pre-image from the image, or vice versa.

How to Perform Translations

When working with translation problems, the information may be presented in different ways.

You may be given a figure drawn on the coordinate plane like this:

Image on coordinate plane

Then you will be asked to translate the figure. You will be given a distance and direction for the transformation.

For example, translate the figure down 7.

The way to do this is to take each vertex point individually and count down 7. So the point at (1, 5) will move to (1, -2). Notice we did not move the vertex along the x-axis, or horizontal direction. The instructions asked us to move it down only, along the y-axis.

Move the other three vertices in the same manner. The point at:

  • (3, 5) moves to (3, -2)
  • (1, 3) moves to (1, -4)
  • (3, 3) moves to (3, -4)

Then connect the vertices to draw the square, translated down 7.

Image translated down 7

Another way that information might be given is like this, starting again with an image drawn on the coordinate plane:

Image on coordinate plane

This time, you will not be asked to draw the translation, but instead to describe it in mathematical notation.

Describe a translation of the triangle down 2 and to the right 3.

The notation will look like this:

(x, y) → (x + 3, y - 2)

To unlock this lesson you must be a Member.
Create your account

Register to view this lesson

Are you a student or a teacher?

Unlock Your Education

See for yourself why 30 million people use

Become a member and start learning now.
Become a Member  Back
What teachers are saying about
Try it risk-free for 30 days

Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Transferring credit to the school of your choice

Not sure what college you want to attend yet? has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

Create an account to start this course today
Try it risk-free for 30 days!
Create an account