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Translation and reflection

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A student claims that anything that can be accomplished by a translation can be accomplished by a reflection. She claims that if A' is the image of A under a translation, then A' can be obtained by a reflection in the line(which is the perpendicular bisector of AA'. Hence, a translation and a reflection are the same. How do you respond?

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The statement requires few add-ons.
If A' is the image of A under a translation, then A' can be obtained by a reflection in the line(which is the perpendicular bisector of AA' - TRUE
But if B' is the image of B under the same ...

Solution Summary

Translation and reflection are discussed.

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Rotations, reflections, translations for Diamond Structure

Please help with the following problems.

The Bravais lattice of the diamond structure is fcc with two carbon atoms per primitive unit cell. If one of the two basis atoms is at (0,0,0), then the other is at (1/4,1/4,1/4).

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(b) Illustrate that a fourfold rotation about an axis in diamond parallel to the x-axis passing through the point (1,1/4,0) (the screw axis) followed by the translation [1/4,0,0] parallel to the screw axis is a screw operation for the diamond structure.

Please explain as clearly as possible.

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