document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=150643>Question 150643</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if (2,4) is the location of the centroid of a triangle. which CANNOT be  the coordinates of the verticles  of the triangle?<BR>\n" );
document.write( "F= (0,0),(0,6),(6,6)<BR>\n" );
document.write( "G=(3,4),(3,-2),(0,6)<BR>\n" );
document.write( "H= (3,-2),(1,6),(2,8)<BR>\n" );
document.write( "J= (2,0) ,(1,8),(3,4) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #110655 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=110655\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The equation for the centroid of a triangle using the vertices coordinates is,<BR>\n" );
document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5Bc%5D ALIGN=MIDDLE  ALT=\"x%5Bc%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5Bc%5D ALIGN=MIDDLE  ALT=\"y%5Bc%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >)=(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29%28x%5B1%5D%2Bx%5B2%5D%2Bx%5B3%5D%29 ALIGN=MIDDLE  ALT=\"%281%2F3%29%28x%5B1%5D%2Bx%5B2%5D%2Bx%5B3%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29%28y%5B1%5D%2By%5B2%5D%2By%5B3%5D%29 ALIGN=MIDDLE  ALT=\"%281%2F3%29%28y%5B1%5D%2By%5B2%5D%2By%5B3%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "or the coordinates must make,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29%28x%5B1%5D%2Bx%5B2%5D%2Bx%5B3%5D%29=2 ALIGN=MIDDLE  ALT=\"%281%2F3%29%28x%5B1%5D%2Bx%5B2%5D%2Bx%5B3%5D%29=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29%28y%5B1%5D%2By%5B2%5D%2By%5B3%5D%29=4 ALIGN=MIDDLE  ALT=\"%281%2F3%29%28y%5B1%5D%2By%5B2%5D%2By%5B3%5D%29=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Let's look at each case,<BR>\n" );
document.write( "F= (0,0),(0,6),(6,6)<BR>\n" );
document.write( "x:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29%280%2B0%2B6%29=2 ALIGN=MIDDLE  ALT=\"%281%2F3%29%280%2B0%2B6%29=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "y:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29%280%2B6%2B6%29=4 ALIGN=MIDDLE  ALT=\"%281%2F3%29%280%2B6%2B6%29=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Set F can be the coordinates, they match the centroid coordinates(2,4).<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "G=(3,4),(3,-2),(0,6)<BR>\n" );
document.write( "x:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29%283%2B3%2B0%29=2 ALIGN=MIDDLE  ALT=\"%281%2F3%29%283%2B3%2B0%29=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "y:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29%284-2%2B6%29=8%2F3 ALIGN=MIDDLE  ALT=\"%281%2F3%29%284-2%2B6%29=8%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Set G cannot be the coordinates, they do not match the centroid coordinates(2,4).<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Let's verify the other two.<BR>\n" );
document.write( "H= (3,-2),(1,6),(2,8)<BR>\n" );
document.write( "x:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29%283%2B1%2B2%29=2 ALIGN=MIDDLE  ALT=\"%281%2F3%29%283%2B1%2B2%29=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "y:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29%28-2%2B6%2B8%29=4 ALIGN=MIDDLE  ALT=\"%281%2F3%29%28-2%2B6%2B8%29=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Set H can be the coordinates, they match the centroid coordinates(2,4).<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "J= (2,0) ,(1,8),(3,4)<BR>\n" );
document.write( "x:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29%282%2B1%2B3%29=2 ALIGN=MIDDLE  ALT=\"%281%2F3%29%282%2B1%2B3%29=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "y:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29%280%2B8%2B4%29=4 ALIGN=MIDDLE  ALT=\"%281%2F3%29%280%2B8%2B4%29=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Set J can be the coordinates, they match the centroid coordinates(2,4).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );