Describing movement on a grid

​​In a nutshell

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.  

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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? 

​$$\underline{(8,8)}$$

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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 $$(5,8)$$.

$$\underline{\begin{pmatrix} 3 \\ -3\end{pmatrix}}$$​​