document.write( "Question 1100667: Please help me solve this question - Find the perimeter of the figure whose vertices are The midpoints of a quadrilateral with vertices at (7,4) (1,8) (-3,4) and (3,-2)
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Algebra.Com's Answer #715260 by ikleyn(52879) $\"\"$ $\"About$

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\n" ); document.write( "It is VERY WELL KNOWN FACT that \"the figure whose vertices are the midpoints of a quadrilateral\" is a parallelogram,
\n" ); document.write( "and the sides of this figure are the mid-segments of triangles diagonals cut the given quadrilateral.\r
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\n" ); document.write( "\n" ); document.write( "See the lesson \r
\n" ); document.write( "\n" ); document.write( " - Midpoints of a quadrilateral are vertices of the parallelogram \r
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\n" ); document.write( "\n" ); document.write( "Therefore, to calculate the perimeter of the \"figure\" and answer the problem's question, all you need to do
\n" ); document.write( "is to find the lengths of two diagonals of the GIVEN quadrilateral and then add them.\r
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\n" ); document.write( "\n" ); document.write( "It can be done in three lines: \r
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document.write( "1)  The length of the diagonal from (7,4) to (-3,4)  is   =  = 10  (! notice this diagonal is vertical segment !).\r\n" );
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document.write( "2)  The length of the diagonal from (1,8) to (3,-2)  is   =  =  =  = .\r\n" );
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document.write( "3)  the sum of the diagonals' lengths is   = 20.198 (approximately), and it is the perimeter of the \"figure\" under the question.\r\n" );
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\n" ); document.write( "\n" ); document.write( "This problem is not about calculations.\r
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\n" ); document.write( "\n" ); document.write( "It is to check whether you know Geometry.\r
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\n" ); document.write( "\n" ); document.write( "And the lesson to learn from this solution IS THIS:\r
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document.write( "    NEVER follow the approach used by @richwmiller when solve problems like this !\r\n" );
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