Points, lines, and even whole shapes can be moved on a grid by a process called translation. Translations move figures on a grid by a specific distance in a specific direction. There are four directions: up, down, left and right.

Translation notation

You write translations in this form $\begin{pmatrix} 5 \\ 4\end{pmatrix}$. The top number is how far along the$x$ axis to move (left and right). The bottom number shows how far along the$y$ axis (up or down) to move an object. This means five units to the right and four units up.

Note: Positive numbers mean move right or up. Negative numbers mean move left or down.

Example 1

On the grid below, translate the point $A(3,4)$ by $\begin{pmatrix} 5 \\ 4\end{pmatrix}$. What are the new coordinates?

$\underline{(8,8)}$

Note: Label the translated point with an apostrophe. In the example above $A$ becomes $A'$.

Describing a translation of a point

You can describe a translation by writing in the format $\begin{pmatrix} x \\ y\end{pmatrix}$ . $x$ represents the top number which is how many units to count left or right along the $x$ axis. $y$ represents the bottom number which is how many boxes you count up or down the $y$ axis.

Example 2

Describe the translation of the point $(8,5)$ to $(5,8)$.