How can the composition of transformations be defined?

The composition of transformations is defined as the process of applying multiple transformations sequentially. This means that one transformation is performed first, and then the second transformation is applied to the result of the first. For example, if you first translate a shape and then rotate it, the final position and orientation of the shape will depend on the combined effect of both transformations.

This definition captures the essence of how transformations can interact and affect a figure's final state. By using composition, you can create complex transformations that can lead to various outcomes based on the order in which they are applied. Each transformation contributes to the overall effect, making it crucial to understand the sequence and type of transformations being used. This foundational concept is vital in geometry and is often explored in greater depth to illustrate how geometric figures can be manipulated in the Cartesian plane.