SOLUTION: Melissa cuts a triangle with vertices at coordinates (0,6) , (4,0), and (8,10). At what point should she place the tip of a pencil to make the triangle balance?

Algebra ->  Triangles -> SOLUTION: Melissa cuts a triangle with vertices at coordinates (0,6) , (4,0), and (8,10). At what point should she place the tip of a pencil to make the triangle balance?      Log On


   

Question 1060781: Melissa cuts a triangle with vertices at coordinates (0,6) , (4,0), and (8,10). At what point should she place the tip of a pencil to make the triangle balance?
Answer by ikleyn(52817) About Me  (Show Source):
You can put this solution on YOUR website!
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Melissa cuts a triangle with vertices at coordinates (0,6) , (4,0), and (8,10). At what point should she
place the tip of a pencil to make the triangle balance?
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At the center of mass of the triangle. 

    The center of mass of a triangle with vertices (x1,y1), (x2,y2) and (x3,y3) is the point (xC,yC) in the coordinate plane  with coordinates

    xC = %28x1%2Bx2%2Bx3%29%2F3,  yC = %28y1%2By2%2By3%29%2F3.

    For the given triangle, the center of mass has the coordinates

    xC = %280%2B4%2B8%29%2F3 = 12%2F3 = 4,  yC = %286%2B0%2B10%29%2F3 = 16%2F3,

    so the point (4,16%2F3) is the center of mass.


    This point is remarkable: it is the common intersection point of three medians of the triangle (for any triangle).

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

Also, you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this online textbook under the topic "Introductory lessons on vectors in a plane".