document.write( "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? \n" ); document.write( "
Algebra.Com's Answer #675669 by ikleyn(52834)\"\" \"About 
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\n" ); document.write( "Melissa cuts a triangle with vertices at coordinates (0,6) , (4,0), and (8,10). At what point should she
\n" ); document.write( "place the tip of a pencil to make the triangle balance?
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\n" ); document.write( "\n" ); document.write( "At the center of mass of the triangle.\r
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document.write( "    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\r\n" );
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document.write( "    xC = \"%28x1%2Bx2%2Bx3%29%2F3\",  yC = \"%28y1%2By2%2By3%29%2F3\".\r\n" );
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document.write( "    For the given triangle, the center of mass has the coordinates\r\n" );
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document.write( "    xC = \"%280%2B4%2B8%29%2F3\" = \"12%2F3\" = 4,  yC = \"%286%2B0%2B10%29%2F3\" = \"16%2F3\",\r\n" );
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document.write( "    so the point (\"4\",\"16%2F3\") is the center of mass.\r\n" );
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document.write( "    This point is remarkable: it is the common intersection point of three medians of the triangle (for any triangle).\r\n" );
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\n" ); document.write( "\n" ); document.write( "See the lesson \r
\n" ); document.write( "\n" ); document.write( "    - The Centroid of a triangle is the Intersection point of its medians \r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-II in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lesson is the part of this online textbook under the topic \"Introductory lessons on vectors in a plane\".\r
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