Transformation of Shapes for GCSE/IGCSE: interactive GeoGebra simulations

 

There are three types of transformations of shapes. They are,

1) Translation

2) Reflection

3) Rotation

In addition, a shape can be enlarged or  diminished by a certain scale factor.

With a set of powerful, yet highly user-friendly  GeoGebra simulations, you can master the transformations while playing around with them on this page.

Translation

To describe a translation, we need a column vector. Its x and y values determine the translation.

With the aid of the following GeoGebra simulation, you can  practise it interactively and learn the concept fast - and enjoy it. You just move the vector by its tip and translate the shape.

Reflection

To describe a reflection, you just need a mirror line. The following GeoGebra simulation help you practise it.

Rotation

To describe a rotation, you need:

a) A centre of rotation

b)  A scale factor

c) The direction - clockwise or anticlockwise

The following GeoGebra animation shows how it works:

Enlargement

In order to describe an enlargement, you need a centre of enlargement and a scale factor, SF.

In the following GeoGebra simulation, you can change the scale factor with the aid of a slider. The centre of enlargement can be changed manually too.

You can click the checkbox to change the polarity of the enlargement - from positive to negative scale factor or vice versa.

Exercises

How to find the Centre of Rotation and Angle of Rotation of a Transformation

In the following image, suppose that the shape, ABC, has been transformed to the shape, A'B'C' by a rotation.

We need to find the centre of rotation and angle of rotation. We can follow the steps below to find both:

Finding the centre of rotation  and angle of rotation

1. Connect the corresponding vertices of both the object and image.
2. Construct the perpendicular bisectors of each line in step 1. The colours of lines match.
3. Find the point where the perpendicular bisectors intersect. That is the centre of rotation.
4. From the centre of rotation, draw two lines to any two corresponding points of the object  and image - B and B' in the above case.
5. Measure the angle between the lines in step 4 and it is the angle of rotation of the transformation.

How to find the Centre of Rotation and Scale Factor of a Transformation

You can find the centre of enlargement and scale factor of an enlargement with the following steps:

Finding the centre of enlargement and scale factor of an enlargement of a shape

1. Connect the corresponding vertices of both the object, ABC  and image, A'B'C'.
2. The point where they intersect at is the centre of enlargement. 
3. Divide the length between centre of enlargement and corresponding points as follows:

SF = OC'/OC = OB'/OB = OA'/OA

How to find the mirror line of a reflection

Finding the mirror line of a reflection of shapes

In this case, you just need to connect corresponding vertices such as B and B'. The perpendicular bisector of any line gives the mirror line of reflection.