# Thread: Identify the rigid motion T o f o T^(-1)

1. ## Identify the rigid motion T o f o T^(-1)

If f is any rigid motion and T is any translation, identify the rigid motion T o f o T^(-1).

Can I split the f into three reflections since there is a theorem that says "Every rigid motion is the composition of at most three relfections and every rigid motion is a translation, a rotation, or a glide relfection"?

My intuition tells me that the final answer would be f by itself since T o T^(-1) will be cancelled out ... I just guess.

2. Originally Posted by rainyice
If f is any rigid motion and T is any translation, identify the rigid motion T o f o T^(-1).

Can I split the f into three reflections since there is a theorem that says "Every rigid motion is the composition of at most three relfections and every rigid motion is a translation, a rotation, or a glide relfection"?

My intuition tells me that the final answer would be f by itself since T o T^(-1) will be cancelled out ... I just guess.
In what form can every translation be written?

3. I have the same exact question actually. I know that every translation is the composition of two reflections with the two axes of reflection being parallel to each other...

4. Originally Posted by Pinkk
I have the same exact question actually. I know that every translation is the composition of two reflections with the two axes of reflection being parallel to each other...
If you don't mind me asking, what class is this for?? Some of your questions suggest you're in an introductory analysis course...but....what's with all the isometry/rigid motion questions? I mean, a couple are a nice supplement to a discussion of mappings but the majority of your questions are these.

5. Introduction to Modern Geometry. First portion of the class is examining Euclid's Postulates and Hilbert's Axioms and classifying/identifying/composing/etc rigid motions.

6. Originally Posted by Pinkk
Introduction to Modern Geometry. First portion of the class is examining Euclid's Postulates and Hilbert's Axioms and classifying/identifying/composing/etc rigid motions.
That's really cool!

7. I'm still completely stuck on this.

8. Originally Posted by Pinkk
I'm still completely stuck on this.
Do you agree with my intuition that the outcome will be f by itself? I viewed this like: go up one block, then go right one block, and then go down one block. The displacement is one block to the right.

9. That's only if $f$ is another translation.

10. Originally Posted by Drexel28
If you don't mind me asking, what class is this for?? Some of your questions suggest you're in an introductory analysis course...but....what's with all the isometry/rigid motion questions? I mean, a couple are a nice supplement to a discussion of mappings but the majority of your questions are these.
do you have any good suggustion to do this problem?