Geometry - position and direction

Describing movement on a grid

Describing movement on a grid

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Tutor: Labib


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 (54)\begin{pmatrix} 5 \\ 4\end{pmatrix}. ​The top number is how far along the xx axis to move (left and right). The bottom number shows how far along the yy 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)A(3,4) by  (54)\begin{pmatrix} 5 \\ 4\end{pmatrix}.  What are the new coordinates? 


Note: Label the translated point with  an apostrophe. In the example above AA​ becomes AA'​. 

Describing a translation of a point

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

Example 2

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

(33)\underline{\begin{pmatrix} 3 \\ -3\end{pmatrix}}​​

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FAQs - Frequently Asked Questions

What can we translate?

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