document.write( "Question 1172331: Find the equation of the line perpendicular to 2x+3y=1 and whose distance from the origin is 7. Please include solutions if you can. Thank you!
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Algebra.Com's Answer #797337 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "The left side of an equation of a line PARALLEL to a given line Ax+By=C has\r\n" );
document.write( "the same left side Ax+By but a different number for C on the right.\r\n" );
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document.write( "The left side of an equation of a line PERPENDICULAR to a given line Ax+By=C\r\n" );
document.write( "has the left side Bx-Ay but a different number for C on the right.\r\n" );
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document.write( "So a line perpendicular to 2x+3y=1 has left side 3x-2y. Let's say it's right\r\n" );
document.write( "side is a number C.\r\n" );
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document.write( "Then we use the formula\r\n" );
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document.write( "Distance from the point (x1,y1)\r\n" );
document.write( "to the line Ax+By+C=0 is\r\n" );
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document.write( "d = \"abs%28Ax%5B1%5D%2BBy%5B1%5D%2BC%29%2Fsqrt%28A%5E2%2BB%5E2%29\"\r\n" );
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document.write( "\"abs%283%280%29-2%280%29%2BC%29%2Fsqrt%28%283%29%5E2%2B%28-2%29%5E2%29=7\"\r\n" );
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document.write( "\"abs%28C%2Fsqrt%289%2B4%29%29=7\"\r\n" );
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document.write( "\"abs%28C%2Fsqrt%2813%29%29=7\"\r\n" );
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document.write( "\"abs%28C%29=7sqrt%2814%29\"\r\n" );
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document.write( "\"C=+%22%22+%2B-+7sqrt%2814%29\"\r\n" );
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document.write( "So there are two solutions:\r\n" );
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document.write( "\"3x-2y=+%22%22+%2B-+7sqrt%2814%29\"\r\n" );
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document.write( "The given line is:\r\n" );
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document.write( "Here is the first line \"3x-2y=+7sqrt%2814%29\" in red.\r\n" );
document.write( "The green line to the origin is 7 units long:\r\n" );
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document.write( "Here is the second line \"3x-2y=+-7sqrt%2814%29\", also in red.\r\n" );
document.write( "The green line to the origin is also 7 units long:\r\n" );
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document.write( "Edwin
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