document.write( "Question 177776: Use analytic geometry to classify the quadrilateral with vertices D(10,0), E(2,4), F(-8,-6), and G(6,-8). Explain your reasoning and show all your work. \n" ); document.write( "
Algebra.Com's Answer #132858 by Fombitz(32388)\"\" \"About 
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\n" ); document.write( "Looks like a kite.
\n" ); document.write( "If it is then,
\n" ); document.write( "\"DE=DG\"
\n" ); document.write( "\"FE=FG\"
\n" ); document.write( "Use the distance formula,
\n" ); document.write( "\"D%5E2=%28x%5B1%5D-x%5B2%5D%29%5E2%2B%28y%5B1%5D-y%5B2%5D%29%5E2\"
\n" ); document.write( "For DE,
\n" ); document.write( "\"D%5E2=%2810-2%29%5E2%2B%280-4%29%5E2\"
\n" ); document.write( "\"D%5E2=64%2B16\"
\n" ); document.write( "\"highlight%28+D=sqrt%2880%29%29%29\"
\n" ); document.write( "For DG,
\n" ); document.write( "\"D%5E2=%2810-6%29%5E2%2B%280-%28-8%29%29%5E2\"
\n" ); document.write( "\"D%5E2=16%2B64\"
\n" ); document.write( "\"highlight%28+D=sqrt%2880%29%29\"
\n" ); document.write( ".
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\n" ); document.write( ".
\n" ); document.write( "For FE,
\n" ); document.write( "\"D%5E2=%28-8-2%29%5E2%2B%28-6-4%29%5E2\"
\n" ); document.write( "\"D%5E2=100%2B100\"
\n" ); document.write( "\"highlight%28+D=sqrt%28200%29%29\"
\n" ); document.write( "For FG,
\n" ); document.write( "\"D%5E2=%28-8-6%29%5E2%2B%28-6-%28-8%29%29%5E2\"
\n" ); document.write( "\"D%5E2=196%2B4\"
\n" ); document.write( "\"highlight%28+D=sqrt%28200%29%29\"
\n" ); document.write( ".
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\n" ); document.write( "We have have proved that the classification is a kite because,
\n" ); document.write( "\"DE=DG\"
\n" ); document.write( "\"FE=FG\"
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