Question

which diagram represents the postulate that states exactly one line exists between any two points?

Explanation:

Step1: Analyze the first diagram

The first diagram has a line with only point \(B\) on it and point \(A\) not on the line. So it does not represent one - line - between - two - points.

Step2: Analyze the second diagram

The second diagram has a line with no points \(A\) or \(B\) on it. So it does not represent one - line - between - two - points.

Step3: Analyze the third diagram

The third diagram has a line with both points \(A\) and \(B\) on it. This represents the postulate that exactly one line exists between any two points.

Step4: Analyze the fourth diagram

The fourth diagram has only two separate points \(A\) and \(B\) with no line connecting them. So it does not represent one - line - between - two - points.

Answer:

The third diagram.