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."
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."
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 ?
Want to join the conversation?
- What can I do to relate to this in my life(126 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(104 votes)
- im confused when it doesnt tell you to expand the circle(57 votes)
- its bc the website probably glitched out or they just forgot to make the circle the size it was supposed to be(26 votes)
- For challenge question 2, how come it isn't the first answer?(12 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(12 votes)
- what will I use this for ?(7 votes)
- How is it -1, 4. It's moving to the right once and moving down 4. Shouldn't the transformation be 1, -4?(5 votes)
- It is a challenge problem because you are moving from C to C', you show movement from C' to C. The prime is always the image, and the non-prime is the preimage.(11 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.
- i like potato chip(9 votes)
- Why is translation, rotation, and reflection needed in real life.(9 votes)