Compositions of Transformations

Composition of Transformations

Multiple Choice

What is the translation rule that follows: T_<5,-9>

• Up 5, Left 9

• Right 5, Up 9

• Left 5, Down 9

• Right 5, Down 9

Intro to Composition of Rigid Motions

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.



Compositions of Equations

We have done compositions of equations in the past.

Example:

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

Compositions of Rigid Motions

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.

Poll

How well does this make sense?

• 1

• 2

• 3

• 4

• 5

Consider the following problem

Open Ended

What is the equation of the line of the previous slide?

Big Idea

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