# Translation Matrices

How to use a translation matrix to find the image under translation: the matrix, example, and its solution.

## Matrix

For the translation (*x*, *y*) → (*x* + *a*, *y* + *b*),

the translation matrix is [*a* / *b*].

To find the coordinates of the image,

add the vertex matrix and the translation matrix:

[*x* / *y*] + [*a* / *b*] = [*x* + *a* / *y* + *b*].

## Example

Previously, you've solved this example.

Translation of a point

Let's solve the same example

by using the tranlation matrix.

Add the vertex matrix and the translation matrix:

[-2 2 0 / 1 3 -1] + [7 7 7 / 5 5 5] = [5 9 7 / 6 8 4].

Then the vertices of the image are*A*'(5, 6), *B*'(9, 8), *C*'(7, 4).

You can see that

by adding the translation matrix, [7 7 7 / 5 5 5],

you can find the vertices of the image,

which is under the translation (*x*, *y*) → (*x* + 7, *y* + 5).