Question

Is it possible that the image of a point after a reflection could be the same point as the preimage? Explain

Answer 1

Yes it is possible if the point is on the line of reflection. For example, if the point (2,0) is reflected over the x axis, then it will stay on the x axis and stay at the location (2,0). 

Answer 2

Certainly.

Every point on the line of reflection is invariant--it maps to itself.