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Question 1105751: In triangle XYZ, point M is the centroid. If XM = 8 which is the length of MA?
Image of the figure - https://prnt.sc/hvnyfm
Answer by ikleyn(52943)   (Show Source):
You can put this solution on YOUR website! .
Answer. MA = 4.
Solution
In any triangle, the medians are concurrent, which means that they have common intersection point, called the centroid.
The centroid divides each median in the ratio 2:1 counting from the corresponding vertex.
For the proof of this geometric fact see the lesson
- Medians of a triangle are concurrent
in this site.
Also, you have this free of charge online textbook on Geometry
GEOMETRY - YOUR ONLINE TEXTBOOK
in this site.
The referred lesson is the part of this online textbook under the topic "Properties of triangles".
Save the link to this online textbook together with its description
Free of charge online textbook in GEOMETRY
https://www.algebra.com/algebra/homework/Triangles/GEOMETRY-your-online-textbook.lesson
to your archive and use it when it is needed.
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By the way, in your plot XA does not seem to be a median . . .
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