document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1154225>Question 1154225</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Help!!!!\r<BR>\n" );
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document.write( "Note that the three medians appear to intersect at the same point! Let's try this out with a particular triangle. Consider the triangle $ABC$ with $A = (3,6)$, $B = (-5,2)$, and $C = (7,-8)$.\r<BR>\n" );
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document.write( "(a) Let $D,$ $E,$ $F$ be the midpoints of $\overline{BC},$ $\overline{AC},$ $\overline{AB},$ respectively. Find the equations of medians $\overline{AD},$ $\overline{BE},$ and $\overline{CF}.$\r<BR>\n" );
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document.write( "(b) Show that the three medians in part (a) all pass through the same point.\r<BR>\n" );
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document.write( "Link of shape: https://latex.artofproblemsolving.com/b/c/3/bc36d6a86ebdd87399c8b07d66ec053e8593c264.png </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #776644 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=776644\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Straightforward, using midpoint formula and slope-intercept form of the equation of a line.  But it is tedious; you need to do the work.<br><BR>\n" );
document.write( "(1) Use the midpoint formula and the given coordinates of A, B, and C to find the midpoints D, E, and F.<BR>\n" );
document.write( "(2) Use the coordinates of A and D to find the slope of AD; then use the slope and one of the points to determine the equation of AD.  Repeat to find the equations of BE and CF.<BR>\n" );
document.write( "(3) Solve the system of any two of the three equations to find their point of intersection; then show that that point satisfies the third equation.<br><BR>\n" );
document.write( "I'll get you started....<br><BR>\n" );
document.write( "D = midpoint of BC = ((-5+7)/2,(2-8)/2) = (1,-3)<br><BR>\n" );
document.write( "slope of AD: (6-(-3))/(3-1) = 9/2<BR>\n" );
document.write( "equation of AD:<BR>\n" );
document.write( "y = mx+b<BR>\n" );
document.write( "-3 = (9/2)(1)+b<BR>\n" );
document.write( "-3 = 9/2+b<BR>\n" );
document.write( "b = -15/2<BR>\n" );
document.write( "y = (9/2)x-15/2<br><BR>\n" );
document.write( "Use the same process to find the equations of BE and CF; then proceed as outlined above.<br><BR>\n" );
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