Question

What does distance preserving mean

Answer 1

Answer: A map f : X → Y is called an isometry or distance preserving if for any a,b ∈ X one has. An isometry is automatically injective; otherwise two distinct points, a and b, could be mapped to the same point, thereby contradicting the coincidence axiom of the metric d.

Explanation:

Answer 2

A rotation is distance preserving. All points in space are rotated but the distance between any 2 points before and after the rotation is preserved.