Is it possible to have 4 lines with 4 intersection points? 4 lines with 5 inter pts? 4 lines with 6 inter pts?

Answer 1

I can get up to 6, but not 7...

For four intersections, imagine two pairs of parallel lines.

For five intersections, imagine one pair of parallel lines.

For six intersections, imagine all lines are skew.

Two lines would cross at a maximum of 1 point.
Three lines would cross at a maximum of 3 points (1 + 2)
(New line forms 2 more intersections with the existing lines.)

Four lines would cross at a maximum of 6 points (1 + 2 + 3).
(New line forms 3 more intersections with the existing lines.)

I've drawn a picture with four lines and 6 intersections.

Answer 2

Yes to all 3 conditions.
Ever play "Pick Up Sticks"?
2 lines can cross a third at different points and a fourth line could cross the first 3 ... that makes 6 intersection points
lay out 4 straws and try it.

Answer 3

when 2 parallel lines intersect 2 other parallel lines perpendicular to the original 2 lines= 4 intersection points.

when 2 parallel lines intersect 2 non parallel lines = 5 intersection points

when 2 non-parallel lines intersect 2 other non-parallel lines= 6 intersection points

Answer 4

The firs line cross nothing. 0
Second line cross 1 line 1
Third line cross 2 lines 2
Fourth line cross 3 lines 3
Sum 6 crossing points

This is the standard situation with no parallel lines.

If fourth line is parallel with the the third, it will cross only 2
lines and then you have 5 crossing points.
If the two first lines is parallel, you take away another crossing point, and you have got 4 of them.
The answer of the questions is then yes!

Answer 5

4 strains with 2 intersections is plausible, as lengthy a you do no longer want all of them to touch. i do no longer think of you've got 4 with 3 strains or 7 with 4. i attempted to artwork it out on paper, yet no longer something is working... :

Answer 6

as long as it is total number of intersecting points.....yes. You can draw this and see it.

Answer 7

if u mean to say TOTAL no. of intersection =4,5 & 6 resp.
Then ,absolutely yes

Answer 8

Yes. There is a way, if you need to see a drawing let me know.