Algebra.Com's Answer #846014 by ikleyn(52784)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "(a) Show that the line containing the points (a, b)and (b, a), where a does not equal b, is perpendicular to the line y = x.
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document.write( "(b) Also, show that the midpoint of (a,b)and (b,a) lies on the line y = x .
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document.write( "(a) The line, containing points (a,b) and (b,a), has the slope\r\n" );
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document.write( "  =  = -1.\r\n" );
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document.write( " The line y = x has the slope  = 1.\r\n" );
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document.write( " Since  = 1*(-1) = -1, the numbers and are opposite reciprocal.\r\n" );
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document.write( " From this, we conclude that these two lines are perpendicular.\r\n" );
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document.write( "(b) The midpoint is ( , ).\r\n" );
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document.write( " Thus you see that x-coordinate of the midpoint is equal to its y-coordinate.\r\n" );
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document.write( " From this, we conclude that the midpoint lies on the line y = x.\r\n" );
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document.write( "At this point, the solution is complete, with all necessary explanations.\r
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