Question

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

Explanation:

Step1: Analyze the first diagram

Only point \(B\) is on the line. So, it does not represent one line through two points \(A\) and \(B\).

Step2: Analyze the second diagram

The line does not pass through point \(B\). So, it does not represent one line through two points \(A\) and \(B\).

Step3: Analyze the third diagram

The line passes through both points \(A\) and \(B\). According to the postulate “exactly one line exists between any two points”, this is the correct representation.

Step4: Analyze the fourth diagram

There is no line drawn. So, it does not represent one line through two points \(A\) and \(B\).

Answer:

The third diagram (the one where the line passes through both points \(A\) and \(B\))