Main content

### Course: High school geometry > Unit 1

Lesson 3: Translations# Translating shapes

In translations, we slide a shape around on a grid. We use the letter "T" to represent translations. We move every point of the shape a certain distance left or right, and up or down, to create a new shape that's the same size and shape as the original. We call the new shape the image.

## Want to join the conversation?

- So... The first # is the x. Then the second one is the y. And when we move those over by how many much they are we go down one too? I'm kind-of lost. (If you can't tell) Can someone please tell me how? I fell dum right now.(30 votes)
- erm what the flip(26 votes)

- never back down never what(28 votes)
- You know on an office building would the windows be an example of a translation?(10 votes)
- Yes, as long as they are identical (same size and shape). That's a good way to look at it!(12 votes)

- i have no clue what im doing in math and im really confused(8 votes)
- You have to use the coordinates given as a guide. So for the transition (8,-1), first what you do is pick a spot where you can move it. So move point A left 8 units because it is on the x-axis and since it is a positive you move it left, if it was negative the point would be moving left.(7 votes)

- Graph a triangle ABC and perform a translation of (x + 4, y − 3) to create triangle A′B′C′.

Describe the transformation using words. Make sure you refer to the characteristics and the coordinates.

Draw a line through points A and A′ and through points B and B′. What do you notice about the lines you drew? Do you think you would notice the same characteristics if you drew another line through points C and C′? How do you know?(6 votes)- I don't know about the graph so I can't give you a specific answer, but you need to translate triangle ABC right 4 units and down 3 units. You should notice the lines between the points are of equal distance.(5 votes)

- When you translate a circle, what part of the circle is translated first?(5 votes)
- Either the central point or the diameter.(2 votes)

- why is a translation called a translation?(3 votes)
- From https://en.wikipedia.org/wiki/Translation

The English word "translation" derives from the Latin word translatio, which comes from trans, "across" + ferre, "to carry" or "to bring" . Thus translatio is "a carrying across" or "a bringing across."

So moving a shape across a grid or from one place to another is translation.(5 votes)

- Bonus question: Triangle 1 is translated. If Triangle 1 has points at
*A = (0,0), B =(3,4), C = (3,0)*, and the distance from A to B' is 15, what are the coordinates of Triangle 1?

(Hints: Use the pythagorean theorem, and try graphing on desmos or geogebra)(5 votes) - 1:50"How do you connect this? Oh there you go" Sal didn't you design this?(3 votes)
- Grown-ups with technology. We're improving to much.(2 votes)

- Im so confused. I'm doing IGCSE and the translation matrix has 4 numbers (0 -1). What do I do?

1 0(3 votes)- transformations with matrices is more a linear algebra concept. You may want to start watching that playlist

You basically multiply the matrix by the coordinates in a column matrix, in that order. using your matrix you mentioned in your question, let's say it is transforming the point (2,3)

|0 -1| * |2|

|1 0| |3|

Do you know how to do matrix multiplication? if not, again take a look at the linear algebra videos, but I could give a basic description.(2 votes)

## Video transcript

- [Voiceover] Triangle ABC
undergoes a translation, and we're using the
notation capital T for it, and then we see what the
translation has to be. We're gonna move, it's kind of small, I hope you can see it on your video screen. We're gonna move positive eight. Every point here is
gonna move positive eight in the x direction. Its x coordinate is going
to increase by eight, or the corresponding point in the image, its x coordinate, is going
to increase by eight, and the corresponding point in the image's y coordinate is going to decrease by
one, so let's do that. And I'll focus on the vertices, whoops, let me drag that to the trash, I didn't mean to do that. I'm going to focus on the vertices well, that's just the
easiest thing for my brain to worth with. And actually, this is what
the tool expects as well. So the point B, is going to move eight to the right, or its corresponding point in the image is going
to have an x coordinate eight larger. So right now, the x
coordinate is negative four, if you added eight to that, it would be positive four, and its y coordinate is going to be one lower. Right now, point B's
y coordinate is eight, one lower than that is seven. So, in the image, the corresponding point of the image would
going to be right over there. And you see we moved eight to the right, and one down. Let's do that with point C. It's at x equals negative seven, if you move eight to the right, if you increase your
x coordinate by eight, you're gonna move to x equals one, and then if you change your y coordinate by negative one, you're
gonna move down one, then you're gonna get to that point right over there. Now, let's do it with point A. So point A's x coordinate is negative one. If you add eight to it, it's going to be positive seven, and its current y coordinate is two. If you take one away from it, you're gonna get to a y coordinate of one. And so there you have it. Let's see, how do I connect these two? Oh, there you go, and we can check our answer. And we got it right. We have performed the translation.