Question

select the postulate that states points a and b lie in only one line.
○ postulate 1b: space contains at least four points not all on one plane.
○ postulate 3: through any three points that are not one line, exactly one plane exists.
○ postulate 2: through any two different points, exactly one line exists.
○ postulate 1: a line contains at least two points.
○ postulate 4: if two points lie in a plane, the line containing them lies in that plane.
○ postulate 5: if two planes intersect, then their intersection is a line.
○ postulate 1a: a plane contains at least three points not all on one line.

Explanation:

The question asks for the postulate stating points A and B lie in only one line. Postulate 2 says through any two different points, exactly one line exists, which matches the description of points A and B being on only one line. Other postulates deal with planes, line - point - plane intersections in different ways, not the uniqueness of the line through two points.

Answer:

Postulate 2: Through any two different points, exactly one line exists.