document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1011927>Question 1011927</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please help me solve this question\r<BR>\n" );
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document.write( "The vertices of a triangle are (1,a)(2,b)(c square,-3):-<BR>\n" );
document.write( "(1) Prove that its centroid cannot lie on the Y - axis.<BR>\n" );
document.write( "(2) Find the condition that the centroid may lie on the X - axis </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #627799 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=627799\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (1) The centroid of a convex polygon is inside the polygon.<BR>\n" );
document.write( "Since The x-coordinates of A, B, and C are all positive number,<BR>\n" );
document.write( "so will be the x-coordinate of the centroid,<BR>\n" );
document.write( "meaning that it will lie to the right of the y-axis.<BR>\n" );
document.write( "Another way;<BR>\n" );
document.write( "The x-coordinate of the centroid is the average of the x-coordinates of the vertices,<BR>\n" );
document.write( "so it is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2B2%2Bc%5E2%29%2F3=%283%2Bc%5E2%29%2F3=1%2Bc%5E2%2F3%3E=1 ALIGN=MIDDLE  ALT=\"%281%2B2%2Bc%5E2%29%2F3=%283%2Bc%5E2%29%2F3=1%2Bc%5E2%2F3%3E=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "so the centroid lies on the line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > or to its right,<BR>\n" );
document.write( "at a distance of at least <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to the right of the y-axis.<BR>\n" );
document.write( " <BR>\n" );
document.write( "(2) The y-coordinate of the centroid is the average of the y-coordinates of the vertices,<BR>\n" );
document.write( "so it is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Bb-3%29%2F3 ALIGN=MIDDLE  ALT=\"%28a%2Bb-3%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "For the centroid to be on the x-axis, that y-coordinate must be zero:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Bb-3%29%2F3=0 ALIGN=MIDDLE  ALT=\"%28a%2Bb-3%29%2F3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bb-3=0 ALIGN=MIDDLE  ALT=\"a%2Bb-3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28a%2Bb=3%29 ALIGN=MIDDLE  ALT=\"highlight%28a%2Bb=3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
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