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 line:
Notice how the line's disposition remained the same as you moved it. Translations only move things from one place to another; they don't change their 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 B\maroonD{B'} by translating B\blueD{B} 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 B\maroonD{B'} by translating B\blueD{B} by 5 units to the right and 4 units down."
More compactly, we can describe this as a translation by 5,4\langle 5,-4 \rangle.
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.

Sources and images

For any transformation, we have the source 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 source point was B\blueD{B} and the image point was B\maroonD{B'}.
Note that we indicated the image by B\maroonD{B'}, pronounced B prime. It is common, when working with transformations, to use the same letter for the image and the source, simply adding the "prime" suffix to the image.

Let's try some practice problems

Problem 1

Problem 2

Problem 3

Challenge problem 1

Challenge problem 2

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