Q: What is the greatest number of intersections that can occur between four lines?

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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.

Related questions

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...

Greatest possible number of intersections for following lines:1(line(s)) = 0 (intersections)2= 13= 1+24= 1+2+35= 1+2+3+4....8=1+2+3+4+5+6+7= 28Every time you add a line, you are able to create 1 more maximum intersection than the previous state. You can add up until 'number of lines - (minus) 1'.

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.]

4

Intersecting lines perform intersections.

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.

There can be a maximum of 15 intersections. With two non-parallel lines, there will be one intersection, a third (non-parallel) line can be drawn to cut the other two, and that makes 2 more intersections for a total of 3. You can actually draw this out, and with a fourth, fifth and sixth line, you will create a maximum of 3, 4 and 5 more intersections (respectively), and this will bring your total to fifteentotal intersections for the six lines. You can get each successive line to cut all of the other existing lines if you draw them in a prejudicial (maximized) way.

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.

The greatest number is six.

The greatest number of intersection points with just four lines is 6.

A sphere.