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The Composition of Geometric Transformations
Concept sheet | Mathematics
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Once each of the geometric transformations have been mastered, they can be used with the same initial figure. In this case, it becomes a composition of transformations.
A composition of transformations is a sequence of transformations.
In terms of notation, for example, |t \circ s| is written "|t| composite |s|" and it means we must perform the reflection first and the translation second. In short, geometric transformations must be carried out from right to left.
Constructing a Composition of Transformations
It is important to follow the composition order presented to acquire the desired image figure.
According to the following drawing:
Perform the composition of transformations |s\circ t|
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Identify the transformation order
Perform the translation |t| and apply a reflection across the axis |s|. -
Perform the first transformation
Perform the translation |t| on the initial figure.
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Perform the second transformation
Perform the reflection on the transformation image and not on the initial figure.
Among all the possible combinations, one has a particular name.
When a composition is made up of a translation and a reflection, and the translation arrow is parallel to the axis of reflection, the composition is called a glide reflection.
In this example, the axis of symmetry |s| is parallel to the translation arrow |t|.
To distinguish between the four basic geometric transformations, observe their properties.
Summary of the Properties of Geometric Transformations