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

In Triangle XYZ Point M Is The Centroid If XM8 Find The Length Of MA class=

Sagot :

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

For the given triangle:

[tex]XM=\frac{2}{3}XA[/tex]

XA is the sum of XM and MA:

[tex]XA=XM+MA[/tex]

Use the two equations above to find MA:

[tex]\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}[/tex]Then, MA is equal to 4
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