Question

State whether it is possible for the figure described to exist. Write yes or no.

Two points both lie in every two lines.

Short answer

No, it is not possible that two points both lie in each of the two lines.

Step-by-step solution

Step 1. Write the postulate 6.

Postulate 6 states that exactly one line passes through any two points.

Step 2. Draw the diagram of the line passing through the two points A and B.

The figure represents a line passing through two points$A$ and$B$ is:

Step 3. State whether it is possible that two points both lie in each of two lines by considering postulate 6 and the above diagram.

From the diagram and postulate 6, it can be noticed that exactly one line can pass through any two points. Therefore, it is not possible that any two points can simultaneously lie on two different lines.

Therefore, it is not possible that two points both lie in each of the two lines.