document.write( "Question 1101452: How many distinct line segments are formed by connecting 1001 collinear points? \n" ); document.write( "

Algebra.Com's Answer #716050 by ikleyn(52795) $\"\"$ $\"About$

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document.write( "Each pair of distinct point creates one and only one unique segment.\r\n" );
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document.write( "We do not consider pairs of coinciding points, since they create degenerated segments.\r\n" );
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document.write( "From the other side, each such a (non-degenerated) segment is created by a pair of distinct points from the given set.\r\n" );
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document.write( "Hence, there is ONE-TO-ONE correspondence between the segments under the question and the pairs of distinct points of the given 1001 points.\r\n" );
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document.write( "It implies that the number of segments under the question is equal to the number of pairs of distinct points, which is \r\n" );
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document.write( " =  =  = 1001*500 = 500500.\r\n" );
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document.write( "Answer. 500500 distinct line segments.\r\n" );
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