Question

in triangle XYZ, point M is the centroid. If XM=8, find the length of MA

Answer 1

Centroid theorem: the centroid is 2/3 of the distance from each vertex to the midpoint of the opposite side.

For the given triangle:

$XM=\frac{2}{3}XA$

XA is the sum of XM and MA:

$XA=XM+MA$

Use the two equations above to find MA:

$\begin{gathered} XM=8 \\ \\ 8=\frac{2}{3}XA \\ \\ XA=\frac{3}{2}(8) \\ \\ XA=12 \\ \\ \\ 12=8+MA \\ MA=12-8 \\ \\ MA=4 \end{gathered}$Then, MA is equal to 4