Rotations

Rotations is exactly what it sounds like. Take an object and then spin it around. But what’s important is where do you spin around?

Consider a merry-go-round. All the horses are rotated around the centre obviously right? In transformations, we give this point a special name: the centre of rotation.

So take the object, identify the centre of rotation, and spin around! In reality, using tracing paper is the most effective way to do it when asked to draw rotations.

The two parameters we need are:

Centre of rotation – (x and y coordinate)
Angle of rotation – usually given as θ

Step by step:
1) Identify your object
2) Place corner of tracing paper on the centre of rotation
3) Mark your object point on the tracing paper
4) Rotate the tracing paper θ degrees in the correct direction
5) Mark your image point on the number plane

Note: (Tracing paper is provided during exams. If you don’t have tracing paper, you can use normal paper, but obviously it’s a little more challenging to see)

Once you have enough practice, you may be able to visualise it mentally and plot the point accordingly.

Try this Geogebra tool to rotate the object around 90°, 180° and 270°. Create your own object and try changing the centre of rotation to see how it affects your image.