Final answer:
Rigid motion does not change the distance between points, as it preserves distances during translations, rotations, and reflections. In one-dimensional motion, it's possible to have zero distance with nonzero displacement when returning to the starting point, or zero displacement with a nonzero distance if the path taken is circuitous.
Step-by-step explanation:
The effect of a rigid motion on the distance between points is that it does not change the distance. A rigid motion refers to any motion in space that preserves distances, meaning the separation between any two points remains constant throughout the motion. Examples of rigid motions include translations (sliding), rotations, and reflections. When discussing the concept of length contraction in physics under the special theory of relativity, the observed shortening of distance as viewed by an observer in motion relative to the points in question is a different phenomenon and occurs only at speeds that are a significant fraction of the speed of light, which are not typical rigid motions observed in everyday life.
Addressing another concept, it is possible for one-dimensional motion to have zero distance but a nonzero displacement. This occurs when an object moves from one position and then returns to the original position, making the overall distance traveled zero but having a displacement of zero since it ends where it started. Conversely, zero displacement occurs when the initial and final positions are the same, even if the path traveled is longer, resulting in a nonzero distance covered. Understanding the difference between distance and displacement is fundamental in kinematics, the branch of mechanics that describes motion.