Mathematical Rotations

This applet investigates mathematical rotations, and is one in series on transformation of shapes. Learn about centres (centers) of rotation, angles of rotation, clockwise and anti-clockwise (counter-clockwise) rotation.

Author and programmer: Ron Barrow

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


Instructions below    Waldomaths video    Worksheet on this topic in .pdf form    See also: Enlargements (Dilations)   Reflections   Translations   Print

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How to Use this Applet

With this program you can investigate rotations of shapes, and the way that they are described. At the start you will see a shape in the centre (the object) and the same shape in a different colour (the image) some distance away from it. The image is a rotation of the object, of 90° anti-clockwise, about the centre of rotation (0,0). You can change the position of the image in two ways: you can either use the slider for changing the angle of rotation, or you can drag the dot at the centre to change the centre of rotation. Try it and see for yourself. At any time you can:
 • change the shape of the object by clicking and dragging its red dots. This will change the image as well
 • show or hide the centre of rotation by ticking or clearing the "Centre" box
 • turn on or off one or two connecting lines (rays) by ticking or unticking their boxes ("Ray 1" and "Ray 2")
 • turn on or off one or two Perpendicular Bisectors of the two rays by ticking or unticking their boxes ("Perp. Bisector 1" and "Perp. Bisector 2") - I'll leave you to discover why!
 • turn on or off the axes or the gridlines by ticking or unticking the "Axes" or "Gridlines" boxes
 • decide whether you want filled solid shapes or empty outlines by ticking or unticking the "Shapes filled" button at the top of the screen
 • 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.