document.write( "Question 566134: In Rhombus ADBC, point A is (6,13) on the coordinate plane, and point B is (13,6) Find the slope-intercept equation of diagonal CD in the rhombus. \n" ); document.write( "
Algebra.Com's Answer #366126 by Edwin McCravy(20086)\"\" \"About 
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document.write( "The rhombus could look like any of these, even the square on the right\r\n" );
document.write( "(a square is a rhombus).  But regardless, the diagonal CD that goes up to\r\n" );
document.write( "the right is always a segment of the same (green) line, and the green\r\n" );
document.write( "line is always perpendicular to the red diagonal, because the diagonals\r\n" );
document.write( "of a rhombus are perpendicular bisectors of each other.\r\n" );
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document.write( "We first find the slope of the red diagonal:\r\n" );
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document.write( "Slope formula\r\n" );
document.write( "m = \"%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29\" with (x1, y1) = (6,13) and (x2, y2) = (13,6)\r\n" );
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document.write( "m = \"%28%286%29-%2813%29%29%2F%28%2813%29-%286%29%29\" = \"%28-7%29%2F%287%29\" = -1\r\n" );
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document.write( "The slope of the green line will have the slope that is formed by\r\n" );
document.write( "inverting \"%28-1%29%2F1\" as \"1%2F%28-1%29\" or -1 and changing the sign to +1\r\n" );
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document.write( "So the slope of the desired green line is +1.\r\n" );
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document.write( "Now we need a point that it goes through.  Since the diagonals of any\r\n" );
document.write( "parallelogram bisect each other, we must find the midpoint of the red\r\n" );
document.write( "diagonal.\r\n" );
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document.write( "Midpoint formula:\r\n" );
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document.write( "Midpoint =  \r\n" );
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document.write( "Midpoint = \r\n" );
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document.write( "Midpoint = \"%28matrix%281%2C3%2C++++++19%2F2%2C+++%22%2C%22%2C+19%2F2%29%29\"   \r\n" );
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document.write( "Now we use the point-slope formula:\r\n" );
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document.write( "y - y1 = m(x - x1)\r\n" );
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document.write( "y - \"19%2F2\" = 1(x - \"19%2F2\")\r\n" );
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document.write( "y - \"19%2F2\" = x - \"19%2F2\"\r\n" );
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document.write( "     y = x\r\n" );
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document.write( "So that's the answer, the equation of the green line.\r\n" );
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document.write( "Edwin
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