0
Still curious? Ask our experts.
Chat with our AI personalities
Jordan
Taiga
SteveAdd your answer:
Earn +20 pts
What is the greatest number of intersections that can occur between four lines?
7
What is the greatest number of intersection points possible with just 5 lines?
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...
How many intersects are there for 4 lines?
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.]
Can four lines have seven intersection points?
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.
How do you find the maximum number of intersections between a given number of lines?
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.
