# Mathematical Translations

This applet investigates mathematical translations, and is one in series on transformations of shapes. Learn about using vector notation to descibe direction and distance of movement.

###### Author and programmer: Ron Barrow

UK Years 7-11, KS3, KS4, Higher and Foundation GCSE Mathematics - Geometry, Shape and Space

TweetInstructions below See also: Enlargements (Dilations) Reflections Rotations Print

## How to Use this Applet

With this program you can investigate **translations of shapes**, and the **vector notation** that is used to describe them. At the start you will see a shape in the centre (the **object**) and the same shape in a different colour (**image 1**) some distance away from it. How far? Well, image 1 is 4 squares to the right and 3 squares up from the object shape, and those figures can be seen in **vector** notation at the top right of the screen. The vector tells us how far and in what direction the object has been shifted, or **translated**, to make image 1. You can change the position of image 1 in two ways: you can either use the sliders for vector 1 on the right, or you can drag image 1 by clicking and dragging the little red circle on one of its points (vertices). Either way the translation and the vector change. If you put a tick by the "Rays 1" box you will see lines going from the object to image 1; the lines join the corresponding vertices on each shape. Try it and see for yourself.

At any time you can:

• change the shape of the object by clicking and dragging its red dots

• introduce a third shape (**image 2**) by ticking its box and drag it by its red dot.

• look at another vector (**vector 2**) by ticking its box - this vector describes the translation from image 1 to image 2

• look at a third vector (**vector 3**) by ticking its box - this vector describes the direct translation from the original object to image 2

• turn on or off the various connecting lines (**rays**) by ticking or unticking their boxes

• turn on or off the axes or the gridlines by ticking or unticking the "Axes" or "Gridlines" boxes

• return to the start position by clicking the "Reset" button at the top of the screen

There is a great deal of investigation to be done using this applet. Enjoy yourself as you learn.