6.2. Can six lines be drawn on a plane so that there are exactly six intersection points? (A point of intersection can be passed through by two or more lines). Justify your answer.
Solution: There are several ways to complete the task. Three of them are illustrated in the figure.

1) Through one point, draw 5 lines, and the 6th one - not parallel to any of them and not passing through the specified point (left figure).
2) Three lines form a triangle, and the other three are parallel to each other and pass through the vertices of the triangle (center figure).
![](https://cdn.mathpix.com/cropped/2024_05_06_9a8365c995f177a984f2g-5.jpg?height=374&width=1506&top_left_y=298&top_left_x=273)

To the solution of problem 6.2

3) Three pairs of parallel lines are drawn as indicated in the right figure.

Answer: Yes.

Recommendations for checking:

| is in the work | points |
| :--- | :--- |
| Correct construction (drawn or described in words) | 7 points |
| Answer without justification, as well as incorrect constructions and/or reasoning that did not lead to the correct solution | 0 points |