document.write( "Question 82987: Find the slope of the line tangent to a circle with center o at (5,3) at point B (-2,5).\r
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Algebra.Com's Answer #59545 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Find the slope of the line tangent to a circle with center \r\n" );
document.write( "O at (5,3) at point B (-2,5). \r\n" );
document.write( "I got: -7/2 \r\n" );
document.write( "Is this right? \r\n" );
document.write( "Thanks\r\n" );
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document.write( "I think you missed a sign. Let's draw the picture:\r\n" );
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document.write( "We can tell that at least you have the sign wrong because lines\r\n" );
document.write( "which go UPHILL TO THE RIGHT have slopes which are POSITIVE and\r\n" );
document.write( "lines which go DOWNHILL TO THE RIGHT have slopes which are NEGATIVE.\r\n" );
document.write( "The tangent line at B goes UPHILL TO THE RIGHT, so it must have a\r\n" );
document.write( "POSITIVE slope, so your negative slope has to be wrong.\r\n" );
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document.write( "First let's find the slope of radius OB:\r\n" );
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document.write( "Use the slope formula:\r\n" );
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document.write( "     y2 - y1\r\n" );
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document.write( "     x2 - x1\r\n" );
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document.write( "where O(x1, y1) = O(5, 3) and B(x2, y2) = B(-2, 5)\r\n" );
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document.write( "     (5) - (3)      2       2\r\n" );
document.write( "m = ——————————— = ———— = - ——— \r\n" );
document.write( "    (-2) - (5)     -7       7 \r\n" );
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document.write( "The radius goes DOWNHILL TO THE RIGHT, so we expected\r\n" );
document.write( "that to have a NEGATIVE slope, and -2/7 is indeed \r\n" );
document.write( "negative.\r\n" );
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document.write( "A tangent line is perpendicular to the radius drawn to\r\n" );
document.write( "the point of tangency.  So the tangent line is \r\n" );
document.write( "perpendicular to a line with slope -2/7.  The rule\r\n" );
document.write( "for finding the slope of a line perpendicular to another\r\n" );
document.write( "line is:\r\n" );
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document.write( "1. Invert the slope.\r\n" );
document.write( "2. Change its sign.\r\n" );
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document.write( "So we take the slope of the radius OB, which is -2/7,\r\n" );
document.write( "then \r\n" );
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document.write( "1. we invert it and get -7/2\r\n" );
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document.write( "and then,\r\n" );
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document.write( "2. we change the sign of -7/2 to +7/2\r\n" );
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document.write( "So the correct answer is +7/2.\r\n" );
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document.write( "Always use the fact that lines with positive slopes\r\n" );
document.write( "go UPHILL to the RIGHT and lines with negative slopes\r\n" );
document.write( "go DOWNHILL to the RIGHT.  That way you won't miss\r\n" );
document.write( "any more signs for slopes if you draw the graphs.\r\n" );
document.write( "You might miss the number but you won't miss the sign!\r\n" );
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document.write( "Edwin

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