document.write( "Question 1178570: A 3 by 5 grid of dots is set out. How many straight line segments can be drawn that join two of these dots and pass through exactly one other dot? \n" ); document.write( "

Algebra.Com's Answer #807885 by ikleyn(52788) $\"\"$ $\"About$

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document.write( "Let think that the grid is 3 points vertically and 5 points horizontally.\r\n" );
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document.write( "Then there are THESE families of straight line segments satisfying imposed conditions\r\n" );
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document.write( "    3 x 3 = 9 horizontal segments of the length 2\r\n" );
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document.write( "            3 horizontal segments of the length 4\r\n" );
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document.write( "            5 vertical segments of the length   2\r\n" );
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document.write( "            1 sloped segment    of the slope   2/4 = 1/2\r\n" );
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document.write( "            3 sloped segments   of the slope     1\r\n" );
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document.write( "            3 sloped segments   of the slope    -1\r\n" );
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document.write( "            1 sloped segment    of the slope  -2/4 = -1/2\r\n" );
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document.write( "Counting this way, there are  9 + 3 + 5 + 1 + 3 + 3 + 1 = 25 segments satisfying the posed condition.\r\n" );
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