document.write( "Question 1008551: a rectangle labeled abcd counter clockwise. point E lies on the diagonal ac such that ae:ac is 4:5. point f lies on the midpoint of cd. express ef in terms of the position vectors oa, ob, oc, and od \n" ); document.write( "

Algebra.Com's Answer #628599 by Fombitz(32388) $\"\"$ $\"About$

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$\"AE%2FAC=4%2F5\"$
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\n" ); document.write( " $\"OD%2B%281%2F2%29%28DC%29=OA%2BAE%2BEF\"$
\n" ); document.write( "or
\n" ); document.write( " $\"EF=OD-OA%2B%281%2F2%29%28DC%29-AE\"$
\n" ); document.write( "Substituting from above,
\n" ); document.write( " $\"EF=OD-OA%2B%281%2F2%29%28DC%29-%284%2F5%29AC\"$
\n" ); document.write( "But you know that
\n" ); document.write( " $\"OA%2BAC=OC\"$
\n" ); document.write( " $\"AC=OC-OA\"$
\n" ); document.write( "So,
\n" ); document.write( " $\"EF=OD-OA%2B%281%2F2%29%28DC%29-%284%2F5%29%28OC-OA%29\"$
\n" ); document.write( "and,
\n" ); document.write( " $\"OD%2BDC=OC\"$
\n" ); document.write( " $\"DC=OC-OD\"$
\n" ); document.write( "So,
\n" ); document.write( " $\"EF=OD-OA%2B%281%2F2%29%28OC-OD%29-%284%2F5%29%28OC-OA%29\"$
\n" ); document.write( " $\"EF=OD-OA%2B%281%2F2%29%28OC%29-%281%2F2%29%28OD%29-%284%2F5%29%28OC%29%2B%284%2F5%29OA%29\"$
\n" ); document.write( " $\"EF=%281%2F2%29OD-%281%2F5%29OA-%283%2F10%29%28OC%29%29\"$
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