Explore BrainMass

# Transformation Geometry Proofs : Reflections

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

Please see the attached file for the fully formatted problems.

Let l, m, n be distinct lines and P, Q, R be distinct points. Prove the following:
(a) sigma l sigma m = sigma m sigma l if and only if l perpendicular to m.
(b) sigma p sigma m = sigma m sigma p if and only if P E m.
plus three more questions

https://brainmass.com/math/geometry-and-topology/transformation-geometry-proofs-reflections-13292

#### Solution Preview

Please see the attached file for the complete solution.
Thanks for using BrainMass.

Proof:
a. If , then we consider a point . We have

So we get . But we know by definition of and . Therefore, we have .
If , we can suppose is the x-axis and is the y-axis. For any point , we have , . Therefore, we get .
b. We can suppose is the x-axis and . We know for any , we have
If , then for any point , we ...

#### Solution Summary

Proofs involving reflections are provided. The solution is detailed and well presented.

\$2.49