Congruence
TODO
Composition of Transformations
Of course, we can combine multiple translations, reflections and rotations to create more complex transformations.
TODO Example
However, as it turns out, it doesn’t matter how many different transformations you combine: you can always find another transformation that does the same in one go!
TODO Transformation composition calculator
Combining two reflections is particularly interesting. There are two different cases we need to consider:
If the two lines of reflection are parallel, the result is a single translation. The direction of the translation is perpendicular to the lines of reflection, and the distance is twice the distance between the lines of reflection.
TODO Animation
If the two lines of reflection intersect, the result is a single rotation. The center of rotation is the intersection between the lines of reflection, and the angle is twice the angle between the lines of reflection.
TODO Animation