document.write( "Question 1203418: solve by addition of line segments show whether the points a(-3,0), b(-1,-1) and c(5,-4) lie on a straight line.\r
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Algebra.Com's Answer #838959 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "The first two tutors did it by slopes and showing they are points on the same\r\n" );
document.write( "line.  Those are valid methods, but the method asked for here is how to do it\r\n" );
document.write( "by addition of line segments.\r\n" );
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document.write( "We use the distance formula to find the length of the line segment from a(-3,0)\r\n" );
document.write( "to b(-1,-1)\r\n" );
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document.write( "\"DISTANCE\"\"%22%22=%22%22\"\"sqrt%28%28x%5B2%5D-x%5B1%5D%29%5E2%2B%28y%5B2%5D-y%5B1%5D%29%5E2%29\"\"%22%22=%22%22\"\"sqrt%28%28-1-%28-3%29%5E%22%22%29%5E2%2B%28-1-0%5E%22%22%29%5E2%29\"\"%22%22=%22%22\"\"sqrt%28%28-1%2B3%5E%22%22%29%5E2%2B%28-1%5E%22%22%29%5E2%29\"\"%22%22=%22%22\"\"sqrt%282%5E2%2B1%29\"\"%22%22=%22%22\"\"sqrt%284%2B1%5E%22%22%29\"\"%22%22=%22%22\"\"sqrt%285%5E%22%22%29\"\r\n" );
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document.write( "Now we use the distance formula also to find the length of the line segment\r\n" );
document.write( "from the point b(-1,-1) to c(5,-4)\r\n" );
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document.write( "\"DISTANCE\"\"%22%22=%22%22\"\"sqrt%28%28x%5B2%5D-x%5B1%5D%29%5E2%2B%28y%5B2%5D-y%5B1%5D%29%5E2%29\"\"%22%22=%22%22\"\"sqrt%28%285-%28-1%29%5E%22%22%29%5E2%2B%28-4-%28-1%29%5E%22%22%29%5E2%29\"\"%22%22=%22%22\"\"sqrt%28%285%2B1%5E%22%22%29%5E2%2B%28-4%2B1%5E%22%22%29%5E2%29\"\"%22%22=%22%22\"\"sqrt%286%5E2%2B%28-3%29%5E2%29\"\"%22%22=%22%22\"\"sqrt%2836%2B9%5E%22%22%29\"\"%22%22=%22%22\"\"sqrt%2845%5E%22%22%29\"\"%22%22=%22%22\"\"sqrt%289%2A5%29\"\"%22%22=%22%22\"\"3sqrt%285%29\"\r\n" );
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document.write( "Now we find the length of the line segment from a(-3,0) to c(5,-4) to see if the\r\n" );
document.write( "sum of those two segments equals to this total length.\r\n" );
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document.write( "\"DISTANCE\"\"%22%22=%22%22\"\"sqrt%28%28x%5B2%5D-x%5B1%5D%29%5E2%2B%28y%5B2%5D-y%5B1%5D%29%5E2%29\"\"%22%22=%22%22\"\"sqrt%28%285-%28-3%29%5E%22%22%29%5E2%2B%28%28-4%29-0%5E%22%22%29%5E2%29\"\"%22%22=%22%22\"\"sqrt%28%285%2B3%5E%22%22%29%5E2%2B%28-4%29%5E2%29\"\"%22%22=%22%22\"\"sqrt%288%5E2%2B16%29\"\"%22%22=%22%22\"\"sqrt%2864%2B16%5E%22%22%29\"\"%22%22=%22%22\"\"sqrt%2880%5E%22%22%29\"\"%22%22=%22%22\"\"sqrt%2816%2A5%29\"\"%22%22=%22%22\"\"4sqrt%285%29\"\r\n" );
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document.write( "And we see that the sum of the two shorter line segments equal to the whole\r\n" );
document.write( "longest line segment:\r\n" );
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document.write( "\"sqrt%285%29\"\"%22%22%2B%22%22\"\"3sqrt%285%29\"\"%22%22=%22%22\"\"4sqrt%285%29\"\r\n" );
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document.write( "That proves that all three points lie on the same line.\r\n" );
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document.write( "Edwin
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