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Composition of Transformations

Composition of Transformations

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Two examples of the idea done right—and one common look-alike that is not right.

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EXAMPLE

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Definition

A composition of transformations is when two or more transformations are performed on a figure in sequence, one after another.

Key Points:

  • Each transformation changes the figure, and the next one is applied to the result of the previous one.

  • Common transformations used in compositions include translations, reflections, rotations, and dilations.

  • The order matters — doing a rotation followed by a reflection usually gives a different result than doing the reflection first.

Example:

If a figure is first reflected over the x-axis and then translated 3 units right, that's a composition of transformations.


A figure, labeled A, and two images, labeled B and C, after multiple transformations in the coordinate plane. A is reflected across the x-axis to form B. B is translated to the right to form C.

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