Math CentralQuandaries & Queries


Question from Cathy, a parent:

This question was on my daughter's geometry assignment. Write a general rule of formula for finding the number of segments that can be named by a given number of points on a line. For example, 2 points on a line = 1 line segment; 3 points on a line = 3 segments; 5 points on a line = 10 segments.


Suppose you look at how many ways you can pick two distinct points. First note that if you pick point a and then point b they determine the same line segment as picking point b first and then point a. If you had 5 points you can pick one of them in 5 ways and then a second point in 4 ways - 20 ways to pick them consecutively, however, from what we've just said, they only determine 10, not 20 segments. If you had 6 points it would lead to (6x5)/2 =15 segments, etc.


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