Question

which diagram represents the postulate that states exactly one line exists between any two points? diagrams: 1) point b on a horizontal line (arrows left/right), point a above; 2) point a and point b with a line (arrow) between; 3) point a and point b on a line (arrow) with a left of b; 4) point a and point b separate, no line

Explanation:

Step1: Understand the Postulate

The postulate states that for any two distinct points, there is exactly one line that passes through both. So we need a diagram where there's a line (could be a line segment, ray, or straight line) connecting points A and B, showing that only one line exists between them.

Step2: Analyze Each Diagram

• First diagram: Point A is separate, line through B. Doesn't connect A and B.
• Second diagram: A ray (or line segment with arrows) connecting point A and point B. This shows a single line (or ray) passing through both A and B, which matches the postulate.
• Third diagram: Line with points A and B on it, but the focus is the line through them, but let's check others. Wait, no—wait the second diagram: A and B are connected by a line (with arrows, maybe a line or ray) directly. The fourth diagram: A and B are separate, no line between. So the second diagram (with A and B connected by a line/ray) represents the postulate.

Answer:

The second diagram (the one with a line/ray connecting point A and point B)