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Given 100 noncollinear points, make a conjecture about the maximum number of lines formed.

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berbs | Student, Grade 9 | Honors

Posted September 11, 2011 at 3:58 AM via web

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Given 100 noncollinear points, make a conjecture about the maximum number of lines formed.

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted September 11, 2011 at 4:15 AM (Answer #1)

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The number of distinct points required to determine a unique line are 2. In the question asked there are 100 non-collinear points. Each of them can determine 99 unique lines with the other points.

But it has to be kept in mind that a line determined by two points A and B is the same even if the position of the points is interchanged, i.e. AB and BA are the same line.

This gives the maximum number of lines that the points can determine as 100*99/2 = 4950

The maximum number of lines that 100 non-collinear points can determine is 4950.

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santaone | High School Teacher | eNoter

Posted September 11, 2011 at 6:45 AM (Answer #2)

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If no three points out of the 100 are colinear then each pair of points will define a separate line.

So first point will define 99 lines and subsequent points will define one line less till the last point which will not define any new line. Therefore total is 99+98+97+.....+1 which works out to

Sum =n(n+1)/2 = 99*100/2 = 4950

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