Composing Geometric Transformations

Composing geometric transformations means applying two or more transformations in a sequence to the same object. $$ s \circ t $$

This is read as "s composed with t," where "s" is the first transformation and "t" is the second.

A Practical Example

For example, let's start with an initial geometric figure.

First, we apply a 90° rotation around the center of rotation, point A.

Next, we apply the second transformation to the result. For instance, a translation along the segment AB.

The final outcome is the composition of these two geometric transformations.

Note: A geometric transformation changes a figure according to specific rules, without altering certain fundamental properties. Examples of geometric transformations include translations, rotations, reflections, and dilations.

It's important to note that the composition of geometric transformations is not commutative.

Therefore, the order in which the transformations are applied is crucial, as it can greatly influence the final result.

And so on.