# Translations intro

CCSS Math: HSG.CO.A.2, HSG.CO.A.4, HSG.CO.A.5

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 $\maroonD{B'}$ by translating $\blueD{B}$ 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 $\maroonD{B'}$ by translating $\blueD{B}$ by 5 units to the right and 4 units down."

More compactly, we can describe this as

**a translation by $\langle 5,-4 \rangle$.**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 $\blueD{B}$ and the image point was $\maroonD{B'}$.Note that we indicated the image by $\maroonD{B'}$, 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.