document.write( "Question 550844: The points A(-1,2),B(x,y) and C=(4,5) are such that BA=BC.Find a linear relation between x and y. \n" ); document.write( "

Algebra.Com's Answer #852297 by ikleyn(52848) $\"\"$ $\"About$

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\n" ); document.write( "The points A(-1,2), B(x,y) and C(4,5) are such that BA=BC. Find a linear relation between x and y.
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\n" ); document.write( "\n" ); document.write( " This problem has a nice Algebra solution.\r
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document.write( "The square of the length of AB is \r\n" );
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document.write( "    |AB|^2 = (x-(-1))^2 + (y-2)^2 = (x+1)^2 + (y-2)^2 = x^2 + 2x + 1 + y^2 - 4y + 4 = x^2 + 2x + y^2 - 4y + 5.\r\n" );
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document.write( "The square of the length of BC is \r\n" );
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document.write( "    |BC|^2 = (x-4)^2 + (y-5)^2 = x^2 - 8x + 16 + y^2 - 10y + 25 = x^2 - 8x + y^2 - 10y + 41.\r\n" );
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document.write( "The condition  |BA| = |BC|  is the same as  |AB|^2 = |BC|^2.  It gives this equation \r\n" );
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document.write( "    x^2 + 2x + y^2 - 4y + 5 = x^2 - 8x + y^2 - 10y + 41.\r\n" );
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document.write( "Combine like terms.  The final equation is\r\n" );
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document.write( "    10x + 6y = 36,\r\n" );
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document.write( "or\r\n" );
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document.write( "    5x + 3y = 18,\r\n" );
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document.write( "or\r\n" );
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document.write( "    y = .    <<<---===  ANSWER\r\n" );
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