document.write( "Question 203940: I need your help about this:
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Algebra.Com's Answer #852454 by ikleyn(53369) $\"\"$ $\"About$

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\n" ); document.write( "Find the equation of the line with points equidistant from (5,-2) and (4,3).
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\n" ); document.write( "\n" ); document.write( " As an alternative to the geometric solution by @Theo, below is simple algebraic solution.\r
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document.write( "Let (x,y) be the point equidistant from these given points (5,-2) and (4,3).\r\n" );
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document.write( "It means that the distances from (x,y) to these points are equal.\r\n" );
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document.write( "Hence, the squares of distances are equal.\r\n" );
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document.write( "So, we write\r\n" );
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document.write( "     +  =  + .\r\n" );
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document.write( "or\r\n" );
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document.write( "     +  =  + .\r\n" );
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document.write( "Now we simplify it\r\n" );
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document.write( "    x^2 - 10x + 25 + y^2 + 4y + 4 = x^2 - 8x + 16 + y^2 - 6y + 9,\r\n" );
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document.write( "    -10x + 4y + 29 = -8x - 6y + 25,\r\n" );
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document.write( "    (-10x + 8x) + (4y + 6y) = 25 - 29,\r\n" );
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document.write( "    -2x + 10y = -4,\r\n" );
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document.write( "     -x +  5y = -2,\r\n" );
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document.write( "      x -  5y = 2.\r\n" );
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