Using the centroid M, the missing values are as follows: MJ = 20, DM = 22, and EL = 18.
In the question, we are given that the medians of the triangle DEF are DK, EL, and FJ, and they meet at the single point M, implying that M is the centroid of the triangle DEF.
Since M is the centroid of the triangle DEF, it divides all the medians in the ratio of 2:1.
Thus, we can write that:
DM/MK = EM/ML = FM/MJ = 2/1.
From this, we get:
DM/MK = 2/1,
or, DM = 2MK,
or, DM = 2*11 = 22 {Since, MK is given to be 11}.
Thus, DM = 22.
EM/ML = 2/1,
or, EM = 2ML,
or, ML = EM/2,
or, ML = 12/2 = 6 {Since, EM is given to be 12}.
Thus, EL = EM + ML = 12 + 6 = 18.
FM/MJ = 2/1,
or, FM = 2MJ.
Now FJ = FM + MJ,
or, FJ = 2MJ + MJ,
or, 3MJ = FJ,
or, MJ = FJ/3,
or, MJ = 60/3 = 20 {Since, FJ is given to be 60}.
Thus, MJ = 20.
Thus, using the centroid M, the missing values are as follows: MJ = 20, DM = 22, and EL = 18.
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