In #\triangle DEF#, #M# is the centroid. (i). Find #\overline{MK}# and #\overline{DK}# #" "# (ii). Find #\overline{LM}# and #\overline{LE}# #" "# (iii). Write an expression for #FJ#?

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1 Answer
CW
Mar 14, 2018

see explanation.

Explanation:

Recall that the centroid of a triangle divides each median in the ratio #1:2# :
#=> DM:MK=2:1#,
#=> 8:MK=2:1, => MK=4#
#=> DK=DM+MK=8+4=12#
SImilarly,
#LM:ME=1:2#,
#=> LM:6=1:2#,
#=> LM=3#,
#=> LE=LM+ME=3+6=9#,
SImilarly,
#FM:MJ=2:1#,
#=> 2x:2y=2:1#,
#=> 2y=x#
#=> FJ=FM+MJ=2x+2y=2x+x=3x#

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