Question

Select the postulate that states a line is determined by two points.

1. Postulate 1: A line contains at least two points.
2. Postulate 1a: A plane contains at least three points not all on one line.
3. Postulate 1b: Space contains at least four points not all on one plane.
4. Postulate 2: Through any two different points, exactly one line exists.
5. Postulate 3: Through any three points that are not one line, exactly one plane exists.
6. Postulate 4: If two points lie in a plane, the line containing them lies in that plane.
7. Postulate 5: If two planes intersect, then their intersection is a line.

Answer 1

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

Explanation:

Answer 2

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

Postulate 2 and Postulate 1 are the only two postulates that really make sense. Postulate 2 is your answer instead of Postulate 1 for the following reason:

Postulate 1 states that a line contains at least two points.
Postulate 2 states that through any two different points, exactly one line exists.

Postulate 1 says that all lines contain at least two points, while Postulate 2 says that two points contain a line.