document.write( "Question 669221: Use coordinate geometry to prove the statement.
\n" ); document.write( "The segments joing the midpoints of a rectangle form a rhombus.
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\n" ); document.write( "A is on the orgin of the coorndiante plan, while D is located on the Y axis.
\n" ); document.write( "B is located on the X axis. C is not n an axis.
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Algebra.Com's Answer #416246 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "The midpoint of AB is E(\"a%2F2\",0),\r\n" );
document.write( "The midpoint of AB is F(\"a%2F2\",\"b%2F2\"),\r\n" );
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document.write( "Using the distance formula, which is:\r\n" );
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document.write( "d = \"sqrt%28%28x%5B2%5D-x%5B1%5D%29%5E2%2B%28y%5B2%5D-y%5B1%5D%29%5E2%29\"\r\n" );
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document.write( "EF = \"sqrt%28%28a-a%2F2%29%5E2%2B%28b%2F2-0%29%5E2%29\" = \"sqrt%28%28a%2F2%29%5E2%2B%28b%2F2%29%5E2%29\"\r\n" );
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document.write( "FG = \"sqrt%28%28a%2F2-a%29%5E2%2B%28b-b%2F2%29%5E2%29\" = \"sqrt%28%28-a%2F2%29%5E2%2B%28b%2F2%29%5E2%29\" = \"sqrt%28%28a%2F2%29%5E2%2B%28b%2F2%29%5E2%29\"\r\n" );
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document.write( "GH = \"sqrt%28%28a-a%2F2%29%5E2%2B%28b%2F2-b%29%29%5E2\" = \"sqrt%28%28-a%2F2%29%5E2%2B%28b%2F2%29%5E2%29\" = \"sqrt%28%28a%2F2%29%5E2%2B%28b%2F2%29%5E2%29\"\r\n" );
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document.write( "HE = \"sqrt%28%28a%2F2-a%29%5E2%2B%280-b%2F2%29%5E2%29\" = \"sqrt%28%28a%2F2%29%5E2%2B%28-b%2F2%29%5E2%29\" = \"sqrt%28%28a%2F2%29%5E2%2B%28b%2F2%29%5E2%29\"\r\n" );
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document.write( "All four sides of EFGH are equal to \"sqrt%28%28a%2F2%29%5E2%2B%28b%2F2%29%5E2%29\" so EFGH is a rhombus.\r\n" );
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document.write( "Edwin
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