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?
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At the center of mass of the triangle.


<pre>
    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 = {{{(x1+x2+x3)/3}}},  yC = {{{(y1+y2+y3)/3}}}.

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

    xC = {{{(0+4+8)/3}}} = {{{12/3}}} = 4,  yC = {{{(6+0+10)/3}}} = {{{16/3}}},

    so the point ({{{4}}},{{{16/3}}}) is the center of mass.


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

See the lesson 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/geometry/The-Centroid-of-a-triangle-is-the-Intersection-point-of-its-medians.lesson>The Centroid of a triangle is the Intersection point of its medians</A> 

in this site.


Also, you have this free of charge online textbook in ALGEBRA-II in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.


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