document.write( "Question 1172220: Find the distance of the line 8x-5y-15=0 from the point (-3,2) \n" ); document.write( "
Algebra.Com's Answer #797170 by ikleyn(52781)\"\" \"About 
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\n" ); document.write( "Find the distance of the line 8x-5y-15=0 from the point (-3,2).
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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 8x - 5y - 15 = 0.\r\n" );
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document.write( "So, the numbers in your case are  a= 8, b= -5, c= -15,  \"x%5B0%5D\" = -3,  \"y%5B0%5D\"= 2.\r\n" );
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document.write( "Substitute the given data  a= 8, b= -5, c= -15,  \"x%5B0%5D\" = -3,  \"y%5B0%5D\"= 2  into the formula to get the distance under the question\r\n" );
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document.write( "    \"abs%288%2A%28-3%29+%2B+%28-5%29%2A2+-+15%29%2Fsqrt%288%5E2%2B%28-5%29%5E2%29\" = \"abs%28-49%29%2Fsqrt%2889%29\" = \"49%2Fsqrt%2889%29\" = \"%2849%2Asqrt%2889%29%29%2F89\" = 5.194  (rounded).\r\n" );
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document.write( "Answer.  The distance is  \"49%2Fsqrt%2889%29\" = \"%2849%2Asqrt%2889%29%29%2F89\" = 5.194  (rounded).\r\n" );
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\n" ); document.write( "\n" ); document.write( "Regarding all details, deducing the formula, illustrations and solutions to other similar problems, see the lessons \r
\n" ); document.write( "\n" ); document.write( "    - The distance from a point to a straight line in a coordinate plane \r
\n" ); document.write( "\n" ); document.write( "    - HOW TO calculate the distance from a point to a straight line in a coordinate plane \r
\n" ); document.write( "\n" ); document.write( "    - Using formula for the distance from a point to a straight line in a plane to solve word problems \r
\n" ); document.write( "\n" ); document.write( "    - OVERVIEW of lessons on the distance from a point to a straight line in a coordinate plane \r
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