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?

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(52824) (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?
~~~~~~~~~~~~~~~~~~~~~~~~

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 = ,  yC = .

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

    xC =  =  = 4,  yC =  = ,

    so the point (,) 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".

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