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## High school geometry

### Course: High school geometry > Unit 1

Lesson 2: Introduction to rigid transformations# Translations intro

CCSS.Math: , ,

Learn what translations are and how to perform them in our interactive widget.

To see what a

**translation**is, please grab the point and move it around.Nice! You

*translated*the point. In geometry, a translation moves a thing up and down or left and right.Here, try translating this segment by dragging it from the middle, not the endpoints:

Notice how the segment's direction and length stayed the same as you moved it. Translations only move things from one place to another; they don't change their size, arrangement, or direction.

Now that we've got a basic understanding of what translations are, let's learn how to use them on the coordinate plane.

## Translations on the coordinate plane

Coordinates allow us to be very precise about the translations we perform.

Without coordinates, we could say something like, "We get start color #ca337c, B, prime, end color #ca337c by translating start color #11accd, B, end color #11accd down and to the right."

But that's not very precise. If we use a coordinate grid, we can say something more exact: "We get start color #ca337c, B, prime, end color #ca337c by translating start color #11accd, B, end color #11accd by 5 units to the right and 4 units down."

More compactly, we can describe this as

**a translation by open angle, 5, comma, minus, 4, close angle.**The negative sign in front of the 4 tells us the vertical shift is downwards instead of upwards. Similarly, a translation to the left is indicated by the first value being negative.

### Pre-images and images

For any transformation, we have the

**pre-image**figure, which is the figure we are performing the transformation upon, and the**image**figure, which is the result of the transformation. For example, in our translation, the pre-image point was start color #11accd, B, end color #11accd and the image point was start color #ca337c, B, prime, end color #ca337c.Note that we indicated the image by start color #ca337c, B, prime, end color #ca337c, pronounced B prime. It is common, when working with transformations, to use the same letter for the image and the pre-image, simply adding the "prime" suffix to the image.

## Let's try some practice problems

### Problem 1

### Problem 2

### Challenge problem

## Want to join the conversation?

- What can I do to relate to this in my life(108 votes)
- Moving. Anything.

If you walk to your door, you're technically translating yourself from where you are to the door, whilst it's in 3D you can still think of walking maybe North 1 meter and West 3 meters, or you could be walking to the store, you go from your house to the store a certain distance one way, then more distance another way which will end up with you in the position of the store. Anytime something moves from one point to another, that's a translation(77 votes)

- Everybody who is here is an omega chad.(51 votes)
- here lies The Cool Kid.(0 votes)

- im confused when it doesnt tell you to expand the circle(35 votes)
- its bc the website probably glitched out or they just forgot to make the circle the size it was supposed to be(15 votes)

- For challenge question 2, how come it isn't the first answer?(11 votes)
- Because if you moved it (1,4), it would end C" would end up 2 spaces to the right, as a movement of (1,4) from point C means the same thing as moving point C 1 space to the right, and four spaces up. The correct answer, answer c, moves point C (-1,4)- 1 space to the left (-1), and 4 spaces up (4). Hope this helps.(17 votes)

- How is this going to help me get a job(8 votes)
- What are the types of translations? Other than left and right and up and down.(3 votes)
- Hi Aidan,

Translations can make an object move only left, only right, only up, only down or a combination of them, such as left & up, left & down.

I hope this helps.

Aiena.(13 votes)

- Why is translation, rotation, and reflection needed in real life.(7 votes)
- this is boring(7 votes)
- Why would it be -1,4 if it is going down?(4 votes)
- It's not going down point C is the starting point and it is moving to create point C'(2 votes)

- But how this help me later in my life?(3 votes)
- It's the basics to a wide range of things used in your everyday life, for example a video, in a video pixels are translating, reflecting and rotating in smooth speeds. The same concept applies to video games which are a big part of my life and many others. So if you think about it these things are already helping you. If you were wondering how this could financially benefit you later in life there are jobs that incorporate this basic concept in a more advanced form like cgi artists, animators and video game devs. Which are pretty cool jobs. I hope this helps you answer your question. If any of my information is incorrect or inaccurate please tell me as I happily take any constructive criticism.(3 votes)