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


Instructions below    Waldomaths video    See also:   Enlargements (Dilations)    Reflections    Rotations   Print

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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.