document.write( "Question 639450: Find the exact directed distance from the line 3x-4y=12 to the point (-2,-1). \n" ); document.write( "
Algebra.Com's Answer #402742 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
Find the exact directed distance from the line 3x-4y=12 to the point (-2,-1).
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document.write( "Use the formula:\r\n" );
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document.write( "The distance from the line Ax+By+C=0 to the point (h,k) is given\r\n" );
document.write( "by the formula\r\n" );
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document.write( "d = ±\"abs%28%28Ah%2BBk%2BC%29%2Fsqrt%28A%5E2%2BB%5E2%29%29%29\" where the sign is the sign\r\n" );
document.write( "of \"B%2FA\" \r\n" );
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document.write( "For your equation\r\n" );
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document.write( "3x-4y=12, first get 0 on the right:\r\n" );
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document.write( "3x-4y-12=0\r\n" );
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document.write( "Then compare to\r\n" );
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document.write( "Ax+By+C=0\r\n" );
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document.write( "and get A=3, B=-4, C=-12, and (h,k) = (-2,-1), so h=-2 and k=-1\r\n" );
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document.write( "\"B%2FA\" = \"%28-4%29%2F3\" = \"-4%2F3\" which is negative, so the\r\n" );
document.write( "directed distance will be negative:\r\n" );
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document.write( "Substituting:\r\n" );
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document.write( "d = ±\"abs%28%28Ah%2BBk%2BC%29%2Fsqrt%28A%5E2%2BB%5E2%29%29\"\r\n" );
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document.write( "d = -\r\n" );
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document.write( "d = -\"abs%28%28-6%2B4-12%29%2Fsqrt%289%2B16%29%29\"\r\n" );
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document.write( "d = -\"abs%28%28-14%29%2Fsqrt%2825%29%29\"\r\n" );
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document.write( "d = -\"abs%28%28-14%29%2F5%29\"\r\n" );
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document.write( "d = -\"14%2F5\" = -2.8\r\n" );
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document.write( "And that green line looks a little shorter than 3 units long.\r\n" );
document.write( "That's only a \"ballpark\" check. But if you compare it to 3\r\n" );
document.write( "units along the x-axis or the y-axis, you'll agree that 2.8\r\n" );
document.write( "is at least close to the length of that green line.\r\n" );
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document.write( "Edwin
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