document.write( "Question 1118777: The graphs of y = -|x-a|+b and y = |x-c|+ d intersect at points (2 , 5)
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Algebra.Com's Answer #734210 by ikleyn(52814) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "It is a \"joke\" problem for advanced students.\r\n" );
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document.write( "It does not assume that you will restore the functions and solve equations.\r\n" );
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document.write( "But it assumes that you firmly know that \r\n" );
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document.write( "    - the first function has a vertex at the point (a,b) with two branches going down perpendicularly and making angles 45 degrees with the axes;\r\n" );
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document.write( "    - the second function has a vertex at the point (c,d) with two branches going up perpendicularly and making angles 45 degrees with the axes.\r\n" );
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document.write( "Then you have a rectangle as the intersection of all the branches (I refer to the solution and the plot / (a sketch is just enough !) \r\n" );
document.write( "by @greenestamps), and the problem asks about  a+c.\r\n" );
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document.write( "Notice that   is x-coordinate of the mid-point of one diagonal of the rectangle,  and it is the same  as x-coordinate \r\n" );
document.write( "of the mid-point of the other diagonal   = 5.\r\n" );
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document.write( "Thus   = 5  and,  hence,  a+c = 10.\r\n" );
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\n" ); document.write( "\n" ); document.write( "This solution is parallel to the final part of the @greenestamps solution,\r
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\n" ); document.write( "\n" ); document.write( "but presented in other words/terms to provide better understanding for you.\r
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\n" ); document.write( "\n" ); document.write( " The major idea of the problem and the major idea of the solution is in that\r
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\n" ); document.write( "\n" ); document.write( " it does not require any calculations (except the absolute minimum).\r
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