Final answer:
The change in the number of regions with the addition of another point on a plane depends on the connectivity with the existing points; no definitive answer can be determined with the given choices without more context.
Step-by-step explanation:
When considering the number of regions that change with the addition of another point on a plane, it does not simply increase by a set factor. The change in number of regions is dependent on how the point is positioned relative to the existing points and how they are connected by lines. Without additional information, a definitive answer cannot be given as multiple scenarios can occur: the number of regions can remain the same if the new point does not connect to form new regions, increase by one if it connects to one existing point, or more if it connects multiple existing points in a way that creates additional regions. However, none of the given scenarios imply a precise rule such as doubling or increasing by any specific factor.