Content code
m1261
Slug (identifier)
the-composition-of-transformations
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Grades
Secondary I
Secondary II
Topic
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.

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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.

Title (level 2)
Constructing a Composition of Transformations
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construction
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It is important to follow the composition order presented to acquire the desired image figure.

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According to the following drawing:

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Perform the composition of transformations |s\circ t|

  1. Identify the transformation order
    Perform the translation |t| and apply a reflection across the axis |s|.

  2. Perform the first transformation
    Perform the translation |t| on the initial figure.

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  1. Perform the second transformation
    Perform the reflection on the transformation image and not on the initial figure.

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Among all the possible combinations, one has a particular name.

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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.

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In this example, the axis of symmetry |s| is parallel to the translation arrow |t|.

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To distinguish between the four basic geometric transformations, observe their properties.

Title (level 2)
Summary of the Properties of Geometric Transformations
Title slug (identifier)
summary
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