Final answer:
If the size of one of the fixed points is reduced by a factor of two, assuming size refers to mass or charge, the strength of the interaction between two fixed points will decrease by a factor of 2.
Step-by-step explanation:
When considering the strength of the interaction between two fixed points, several factors need to be considered, such as the nature of the interaction. For gravitational and electrostatic forces, the strength of the interaction is dictated by the properties of the two objects (i.e., their masses or charges) and the distance between them. If you reduce the size of one of them, and by size, we refer to reducing the charge or mass of one of these fixed points, the law dictates that the interaction between the two points is proportional to the product of their charges or masses. Therefore, if the size, or more specifically the charge or the mass of one object, is reduced by a factor of two, the strength of the interaction between the two fixed points will decrease by the same factor of 2 (options a), assuming that distance is not a variable in this scenario. However, to give a definitive answer, we need to clarify the context and the specific nature of the 'strength' referred to in the question (i.e., gravitational, electrostatic, magnetic, etc.).