Hello meggnogI assume from your question that you are given three (non-collinear) points A, B, C on the original object, and their images f(A), f(B), f(C). Then the process is something like:

- Look first at the
sensein which the original points and their images are ordered: in other words, whether they are arranged in clockwise or anticlockwise order in the object and its image. If they are inoppositesenses (i.e one is clockwise and the other anti-clockwise), then the isometry is a reflection or a glide reflection.

To distinguish between a reflection and a glide reflection, join pairs of corresponding points: A to f(A), etc. If all three of these lines are parallel, then it's a simple reflection; if not, it's a glide reflection.

.- If, conversely, the sense of the points and their images are the
same(i.e. both clockwise or both anti-clockwise) then it's either a translation or a rotation.

To distinguish between them, again you can join pairs of corresponding points. If all three lines are parallel, then it's a translation; if not, it's a rotation.

Grandad