SOLUTION: In a plot, a triangle ABC is formed with its vertex, A(2,0), B(3,-2), and C(7,5). What is the intersection of the medians?

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Question 1082349: In a plot, a triangle ABC is formed with its vertex, A(2,0), B(3,-2), and C(7,5). What is the intersection of the medians?
Answer by ikleyn(52781) About Me  (Show Source):
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The intersection of medians of a triangle is the "center of masses" of the triangle.


It is also called "centroid" and/or "barycenter".


Very well and widely known fact is that this point has coordinates (Xc,Yc), where

Xc = %28x%5B1%5D+%2B+x%5B2%5D+%2B+x%5B3%5D%29%2F3,
Yc = %28y%5B1%5D+%2B+y%5B2%5D+%2B+y%5B3%5D%29%2F3.

In our case,  Xc = %282%2B3%2B7%29%2F3 = 12%2F3 = 4  and  Yc = %280-2%2B5%29%2F3 = 3%2F3 = 1.


So, the intersection of medians is the point (4,1).

See the lesson
    - The Centroid of a triangle is the Intersection point of its medians
in this site.

This lesson contains a list of associated lessons than might be interesting for you, too.