Geometry (all content)
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 by translating down and to the right."
A pre-image point labeled B at the top left of the space. The image point labeled B prime is down and to the right of the pre-image.
But that's not very precise. If we use a coordinate grid, we can say something more exact: "We get by translating by 5 units to the right and 4 units down."
Point B is translated five units to the right and four units down to form B prime.
More compactly, we can describe this as a translation by .
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 and the image point was .
Note that we indicated the image by , 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
Each unit in the grid equals .
Draw the image of the line segment under a translation by .
Each unit in the grid equals .
Draw the image of the circle after a translation by .
What translation maps point to point ?
2 points on a coordinate plane. The x- and y- axes scale by one. The pre-image point is labeled C. The image point labeled C prime is located left one unit from the pre-image and up four units.
Want to join the conversation?
- What can I do to relate to this in my life(110 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(81 votes)
- Everybody who is here is an omega chad.(56 votes)
- Guys! I am The Cool Kid's alt! If you don't believe me, look up @TheCoolKid298, click the link, and watch the video!(3 votes)
- im confused when it doesnt tell you to expand the circle(37 votes)
- its bc the website probably glitched out or they just forgot to make the circle the size it was supposed to be(17 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.
- this is boring(8 votes)
- Why is translation, rotation, and reflection needed in real life.(7 votes)
- How am I gonna use this in the real world?(4 votes)
- Maybe if you are building something or creating art or digital art or graphics. If you lay tile, it is important. I do not know what all you might do in the future.(5 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'(3 votes)