# Euclidean Metric : Translation and Rotation

Let be the standard euclidean metric on defined by

where and are any points in .

a) a translation is a map given by

for some fixed given point . Prove, that the Euclidean metric d on is translation-invariant, ie, for any translation T it follows:

.

b) A rotation is a map given by

for some fixed real number . Prove, that the Euclidean metric d on is rotation-invariant, ie, for any rotation it follows:

.

© BrainMass Inc. brainmass.com October 9, 2019, 5:15 pm ad1c9bdddfhttps://brainmass.com/math/synthetic-geometry/euclidean-metric-translation-rotation-52031

#### Solution Preview

Please see the attached file for the complete solution.

Thanks for using BrainMass.

Let be the standard euclidean metric on defined by

where and are any points in .

a) a translation is a map given by

for some fixed ...

#### Solution Summary

Translation and rotation of a Euclidean metric are investigated. The solution is detailed and well presented.