document.write( "Question 849893: From A(0,1),B(2,1),C(4,3) and D(-2,5). Find the values of r and s if rAD + sCD =AB \n" ); document.write( "
Algebra.Com's Answer #511877 by AnlytcPhil(1806)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Some information is missing because that equation has two variables,\r\n" );
document.write( "and there must be enough information to get another equation in order\r\n" );
document.write( "to find a definite value for both variables.  We can find all the\r\n" );
document.write( "distances so that the three lines' lengths are known, but that is\r\n" );
document.write( "as far as we can take it without the missing information.  You may\r\n" );
document.write( "post the missing information in the thank you note.  But here are how\r\n" );
document.write( "to find the lengths of the three lines in the one equation: \r\n" );
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document.write( "Use the distance formula to find the length of AD\r\n" );
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document.write( "d = √(x2-x1)²+(y2-y1)² \r\n" );
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document.write( "where (x1,y1) = (0,1), (x2,y2) = (-2,5),  \r\n" );
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document.write( "AD = √(-2-0)²+(5-1)² = √(-2)²+(4)² = √4+16 = √20 = √4·5 = 2√5\r\n" );
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document.write( "Use the distance formula to find the length of CD\r\n" );
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document.write( "d = √(x2-x1)²+(y2-y1)² \r\n" );
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document.write( "where (x1,y1) = (4,3), (x2,y2) = (-2,5),  \r\n" );
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document.write( "AD = √(-2-4)²+(5-3)² = √(-6)²+(2)² = √36+4 = √40 = √4·10 = 2√10\r\n" );
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document.write( "Use the distance formula to find the length of AB.\r\n" );
document.write( "(We can look and see that this line has length 2.  But we'll\r\n" );
document.write( "use the formula anyway:\r\n" );
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document.write( "d = √(x2-x1)²+(y2-y1)² \r\n" );
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document.write( "where (x1,y1) = (0,1), (x2,y2) = (2,1),  \r\n" );
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document.write( "AB = √(-2-0)²+(1-1)² = √(-2)²+(0)² = √4+0 = √4 = 2\r\n" );
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document.write( "rAD + sCD = AB\r\n" );
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document.write( "r·2√5 + s·2√10 = 2\r\n" );
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document.write( "or\r\n" );
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document.write( "2r√5 + 2s√10 = 2\r\n" );
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document.write( "And we can divide that equation through by 2:\r\n" );
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document.write( "r√5 + s√10 = 1\r\n" );
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document.write( "That's as far as we can go without the missing information.\r\n" );
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document.write( "Edwin
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