document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=127647>Question 127647</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 5. Position a triangle ABC on a graph so the point A is at (0, 0), point B is at (a, 0) and point C is at (b, c). Compute the midpoints of sides AC and BC. Show that the length of the line segment connecting these midpoints is one half of the length of side AB and show that this line segment is parallel to side AB.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #93532 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=93532\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's a drawing:\r<BR>\n" );
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document.write( "Let's find the midpoint of AC:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%280%2Bc%29%2F2=c%2F2 ALIGN=MIDDLE  ALT=\"y=%280%2Bc%29%2F2=c%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the midpoint of AC is (b/2, c/2)\r<BR>\n" );
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document.write( "Let's find the midpoint of BC:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%280%2Bc%29%2F2=c%2F2 ALIGN=MIDDLE  ALT=\"y=%280%2Bc%29%2F2=c%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the midpoint of BC is (a+b/2, c/2)\r<BR>\n" );
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document.write( "Now let's compute the length of line that connects the two midpoints\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=sqrt%28%28x%5B2%5D-x%5B1%5D%29%5E2%2B%28y%5B2%5D-y%5B1%5D%29%5E2%29 ALIGN=MIDDLE  ALT=\"L=sqrt%28%28x%5B2%5D-x%5B1%5D%29%5E2%2B%28y%5B2%5D-y%5B1%5D%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=sqrt%28%28b%2F2-%28a%2Bb%29%2F2%29%5E2%2B%28c%2F2-c%2F2%29%5E2%29 ALIGN=MIDDLE  ALT=\"L=sqrt%28%28b%2F2-%28a%2Bb%29%2F2%29%5E2%2B%28c%2F2-c%2F2%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in the points of the midpoints\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=sqrt%28%28-a%2F2%29%5E2%2B0%5E2%29 ALIGN=MIDDLE  ALT=\"L=sqrt%28%28-a%2F2%29%5E2%2B0%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms and simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=sqrt%28a%5E2%2F4%29 ALIGN=MIDDLE  ALT=\"L=sqrt%28a%5E2%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-a%2F2 ALIGN=MIDDLE  ALT=\"-a%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=a%2F2 ALIGN=MIDDLE  ALT=\"L=a%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2F4 ALIGN=MIDDLE  ALT=\"a%5E2%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since we can see that the length of AB is a (ie it's \"a\" units from the origin), this shows us that the length of the line that connects the two midpoints is half of AB\r<BR>\n" );
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document.write( "------------------------------------------------------------\r<BR>\n" );
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document.write( "Now let's find the slope of the line that connects the two midpoints\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%28y%5B1%5D-y%5B2%5D%29%2F%28x%5B1%5D-x%5B2%5D%29 ALIGN=MIDDLE  ALT=\"m=%28y%5B1%5D-y%5B2%5D%29%2F%28x%5B1%5D-x%5B2%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=%28c%2F2-c%2F2%29%2F%28b%2F2-%28a%2Bb%29%2F2%29 ALIGN=MIDDLE  ALT=\"m=%28c%2F2-c%2F2%29%2F%28b%2F2-%28a%2Bb%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in the given points\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=0%2F%28-a%2F2%29 ALIGN=MIDDLE  ALT=\"m=0%2F%28-a%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms and simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=0 ALIGN=MIDDLE  ALT=\"m=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide\r<BR>\n" );
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document.write( "So the slope between the two midpoints is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=0 ALIGN=MIDDLE  ALT=\"m=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Remember, a slope of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=0 ALIGN=MIDDLE  ALT=\"m=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > means that the line is horizontal. Since AB is also horizontal, the two lines are parallel.\r<BR>\n" );
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