In ∆def, the midpoint of the side opposite vertex d is m and the centroid is c. if dm is 6, what is dc and cm?

DC = 4

CM = 2

Step-by-step explanation:

Remark

The centroid is located at the intersection point of all three medians of a triangle. The centroid is divides the median into a ratio of 2 to 1. The 1 is located closest to the intersection point of the median and the side opposite the vertex which is the starting point of the median.  

In this particular triangle  CM<DC

Givens

DC + CM = 6

CM <DC                  Labeled.

Set up Proportion

1:3 :: MC : (DC + CM)

1:3 :: MC : 6            

1/3 = MC/6              Cross Multiply

3*MC = 6                 Divide by 3

MC = 6/3                 Divide

Answer

MC = 2

DC = 6 -2 = 4

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step-by-step explanation: