In $△ D E F$ $\triangle DEF$ , $M$ $M$ is the centroid. (i). Find $¯ ¯¯¯¯¯¯ ¯ M K$ $\overline{MK}$ and $¯ ¯¯¯¯¯ ¯ D K$ $\overline{DK}$ $" "$ (ii). Find $¯ ¯¯¯¯¯ ¯ L M$ $\overline{LM}$ and $¯ ¯¯¯¯ ¯ L E$ $\overline{LE}$ $" "$ (iii). Write an expression for $F J$ $FJ$ ?

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In $△ D E F$ $\triangle DEF$ , $M$ $M$ is the centroid. (i). Find $¯ ¯¯¯¯¯¯ ¯ M K$ $\overline{MK}$ and $¯ ¯¯¯¯¯ ¯ D K$ $\overline{DK}$ $" "$ (ii). Find $¯ ¯¯¯¯¯ ¯ L M$ $\overline{LM}$ and $¯ ¯¯¯¯ ¯ L E$ $\overline{LE}$ $" "$ (iii). Write an expression for $F J$ $FJ$ ?

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Answer 1 · 2018-03-14T01:35:58

see explanation.

Explanation:

Recall that the centroid of a triangle divides each median in the ratio $1 : 2$ $1:2$ :
$\Rightarrow D M : M K = 2 : 1$ $=> DM:MK=2:1$ ,
$\Rightarrow 8 : M K = 2 : 1, \Rightarrow M K = 4$ $=> 8:MK=2:1, => MK=4$
$\Rightarrow D K = D M + M K = 8 + 4 = 12$ $=> DK=DM+MK=8+4=12$
SImilarly,
$L M : M E = 1 : 2$ $LM:ME=1:2$ ,
$\Rightarrow L M : 6 = 1 : 2$ $=> LM:6=1:2$ ,
$\Rightarrow L M = 3$ $=> LM=3$ ,
$\Rightarrow L E = L M + M E = 3 + 6 = 9$ $=> LE=LM+ME=3+6=9$ ,
SImilarly,
$F M : M J = 2 : 1$ $FM:MJ=2:1$ ,
$\Rightarrow 2 x : 2 y = 2 : 1$ $=> 2x:2y=2:1$ ,
$\Rightarrow 2 y = x$ $=> 2y=x$
$\Rightarrow F J = F M + M J = 2 x + 2 y = 2 x + x = 3 x$ $=> FJ=FM+MJ=2x+2y=2x+x=3x$

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In $△ D E F$ $\triangle DEF$ , $M$ $M$ is the centroid. (i). Find $¯ ¯¯¯¯¯¯ ¯ M K$ $\overline{MK}$ and $¯ ¯¯¯¯¯ ¯ D K$ $\overline{DK}$ $" "$ (ii). Find $¯ ¯¯¯¯¯ ¯ L M$ $\overline{LM}$ and $¯ ¯¯¯¯ ¯ L E$ $\overline{LE}$ $" "$ (iii). Write an expression for $F J$ $FJ$ ?

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