Please help very hard trig. Question? Thanks.?

Question

If I have a point and its image, is that enough to determine whether the image was found using a translation, reflection, rotation, or glide reflection?”

Answer 1

No, I would say it's not.

Example:

Let the original point be (1,1)
Let my image point be (-1,-1)

I can think of 3 different translations off the top of my head to get from Original to image:

Translation by the vector (-2,-2)
Reflection about the x-axis followed by reflection about the y-axis
Rotation by 180° in either direction

If you had a set of points, it would be easier to tell which translation was used, but a single point is too easily manipulated for determination of exactly what translation was used.