document.write( "Question 319054: Can you find the coordinates of B given A(3,8) and M(5,4)?
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Algebra.Com's Answer #228403 by Edwin McCravy(20055) $\"\"$ $\"About$

You can put this solution on YOUR website!
Can you find the coordinates of B given A(3,8) and M(5,4)?
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document.write( "There are two ways.  We'll do both.\r\n" );
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document.write( "Graphically:\r\n" );
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document.write( "Draw the right triangle with one leg vertical and one leg \r\n" );
document.write( "horizontal that has AM as its hypotenuse:\r\n" );
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document.write( "Notice that the vertical leg is 4 units and the horizontal leg is 2 units\r\n" );
document.write( "long.  So duplicate that triangle below, and you have this, so you see that\r\n" );
document.write( "M(5,4) is the midpoint between A(3,8) and B(7,0).\r\n" );
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document.write( "Second way:\r\n" );
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document.write( "Let B have the coordinates B(, )\r\n" );
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document.write( "Then use the midpoint formula:\r\n" );
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document.write( "Midpoint between (,) and  (, )\r\n" );
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document.write( "is   = (5,4)\r\n" );
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document.write( "Let A(3,8) = (,)\r\n" );
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document.write( "so that , and \r\n" );
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document.write( "Let B have the coordinates B(, )\r\n" );
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document.write( "Then  \r\n" );
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document.write( "and\r\n" );
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document.write( "So you have the system of equations\r\n" );
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document.write( "Multiply both equations through by 2\r\n" );
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document.write( "Solve each and get:\r\n" );
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document.write( "So M(5,4) is the midpoint between A(3,8) and B(7,0).\r\n" );
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document.write( "Do it whichever way your teacher wants.\r\n" );
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document.write( "Edwin

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