Question 353824: would you please help me for this question?and thanks for advance!
Lines are drawn through each pair of set of points, no three of which are collinear. If the number of points is doubled, the number of lines is increased by 210. How many points are in the original set?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Lines are drawn through each pair of set of points, no three of which are collinear. If the number of points is doubled, the number of lines is increased by 210. How many points are in the original set?
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Let the original # of points be "n".
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Then # of lines is nC2 = n(n-1)/2
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New # of points is "2n".
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Then # of line is 2nC2 = (2n)(2n-1)/2
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Equation:
new # of lines - original # of lines = 210
(2n)(2n-1)/2 - n(n-1)/2 = 210
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2n(2n-1) - n(n-1) = 420
4n^2-2n - n^2 + n = 420
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3n^2 -n - 420 = 0
(3n+35)(n-12) = 0
Positive solution:
n = 12
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Cheers,
Stan H.
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