document.write( "Question 1174470: Find the distances of the point (4,-2) from the line 2x+3y-6=0​ \n" ); document.write( "
Algebra.Com's Answer #799894 by ikleyn(52878)\"\" \"About 
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document.write( "There is a remarkable formula to calculate the distance from a given point to a given straight line in a coordinate plane.\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 = (\"x%5B0%5D\",\"y%5B0%5D\") 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 = \"abs%28a%2Ax%5B0%5D+%2B+b%2Ay%5B0%5D+%2B+c%29%2Fsqrt%28a%5E2+%2B+b%5E2%29\".\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" );
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document.write( "Your straight line is 2x + 3y - 6 = 0.   The point is  (4,-2)\r\n" );
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document.write( "Substitute the given data  a= 2, b= 3, c= -6,  \"x%5B0%5D\" = 4,  \"y%5B0%5D\"= -2  into the formula to get the distance under the question\r\n" );
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document.write( "    \"abs%282%2A4+%2B+3%2A%28-2%29+-+6%29%2Fsqrt%282%5E2+%2B+3%5E2%29\" = \"abs%28-4%29%2Fsqrt%2813%29\" = \"4%2Fsqrt%2813%29\" = \"%284%2Asqrt%2813%29%29%2F13\" = 1.1094  (approximately).\r\n" );
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document.write( "Answer.  The distance is  \"%284%2Asqrt%2813%29%29%2F13\" = 1.1094  (approximately).\r\n" );
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