Chat with our AI personalities
Well...lines go in one direction forever,but LINE SEGMENTS are a whole different story.With line segments you can make as much intersections as you want but with lines,only 1.
10. Each additional line can only intersect each of the previous lines once, so for two lines, there can be only 1 intersection, for three there can be up to 3 intersections (1+2), for four there can be up to 6 intersections (3+3), and for five there can be up to 10 (6+4). This trend continues as you increase the number of lines: 6 lines: 15 possible intersections (10+5) 7 lines: 21 possible intersections (15+6) 8 lines: 28 possible intersections (21+7) and so on...
Maximum 12 intersections are there! You can simply use the formula: No. of intersections = n(n-1)/2 [where 'n' is the number of lines] This is derived as each new line can intersect (at most) all the previously drawn lines. There if there is: 1 line => 0 intersections 2 lines => 1 intersection 3 lines => 3 intersections [1 that was there + 2 by the new line can intersect both the previous lines.] 4 lines => 6 intersections [3 that were already there + 3 because the new line can intersect all the 3 lines that were present previously.]
No. In plane geometry, two lines can intersect at at most one point. This means that for n points, the maximum number of intersections is limited by the number of pairs of lines. For lines a,b,c,d, there are six pairs: (a,b), (a,c), (a,d), (b,c), (b,d), (c,d). So four lines can have at most six intersections.
Use the formula (n2 - n)/2 where n is the given number of lines. That gives: (12 - 1)/2 = 0 for one line, (22 - 2)/2 = 1 for two lines, (32 - 3)/2 = 3 for three lines, (42 - 4)/2 = 6 for four lines, (52 - 5)/2 = 10 for five lines, and so on.