document.write( "Question 1160834: Find the point on the line y=5x+1 that is closest to the point (3,5) . \n" ); document.write( "

Algebra.Com's Answer #784266 by ikleyn(52790) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( " I will present here another way to solve the problem.\r
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document.write( "On the line (x,5x+1) we want to find the point closest to (3,5).\r\n" );
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document.write( "Write the distance formula (the square of distance formula)\r\n" );
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document.write( "    d^2 = (x-3)^2 + (5x+1-5)^2 = \r\n" );
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document.write( "          (x-3)^2 + (5x-4)^2 = x^2 - 6x + 9 + 25x^2 - 40x + 16 = \r\n" );
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document.write( "                             = 26x^2 - 46x + 25.\r\n" );
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document.write( "The minimum of this quadratic form is at  x =  =  = .\r\n" );
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document.write( "ANSWER.  The closest point is  ( , ) = ( , ).\r\n" );
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