document.write( "Question 1195476: What is the distance of the shortest path between the line y=2x + 12 and the point (5,3)? \n" ); document.write( "

Algebra.Com's Answer #827972 by ikleyn(52797) $\"\"$ $\"About$

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\n" ); document.write( "What is the distance of the shortest path between the line y=2x + 12 and the point (5,3)?
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document.write( "All you need to do is to find the distance from the point (5,3) to the given straight line  y = 2x + 12.\r\n" );
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document.write( "Write equation of the line in EQUIVALENT form  2x - y + 12 = 0.\r\n" );
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document.write( "There is a remarkable formula which ideally suits for this problem.\r\n" );
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document.write( "    Let the straight line in a coordinate plane is defined in terms of its linear equation \r\n" );
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document.write( "         a*x + b*y + c = 0,\r\n" );
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document.write( "    where \"a\", \"b\" and \"c\" are real numbers, and let P = (,) be the point in the coordinate plane. \r\n" );
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document.write( "    Then the distance from the point P to the straight line is equal to\r\n" );
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document.write( "        d = .\r\n" );
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document.write( "Regarding this formula, see the lesson\r\n" );
document.write( "    The distance from a point to a straight line in a coordinate plane\r\n" );
document.write( "in this site.\r\n" );
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document.write( "Substitute the coefficients  a= 2, b= -1, c= 12,   = 5,  = 3  into the formula to get the distance under the question\r\n" );
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document.write( "    d =  = .\r\n" );
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document.write( "Answer.  The distance from the point to the line is   =  = 8.497  (rounded).\r\n" );
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