Composition of Transformations

What we are going to be talking about today is compositions of rigid motions. 

Compositions of rigid motions is the idea of doing two or more rigid motions to the same object. So for instance, I can translate an object and then reflect it. We represent compositions with a hollow circle.



We have done compositions of equations in the past.

Example:

If f(x)=x+1 and g(x)= x²-1. Find (f∘g)(x).

Example:

(R_m∘T_<-2,-5>)(∆ABC)

This means we are going to Translate the triangle ABC 2 units to the left and 5 units down. Then we are going to reflect it across the line l. 

Like equations we do read this from right to left.

A composition over two parallel lines will result in a translation!