document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1137449>Question 1137449</A>: <I><SPAN STYLE=\"word-break: break-all;\"> do the diagonals of ABCD bisect each other?\r<BR>\n" );
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document.write( "A(-1,-7),  B(-3,-5),  C(-2,2),  D(0,0)\r<BR>\n" );
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document.write( "There is nothing in my notes on this and I emailed my teacher asking for help. So any help is appreciated. Thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #755325 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=755325\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If a quadrilateral is a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=parallelogram ALIGN=MIDDLE  ALT=\"parallelogram\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then the diagonals <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=bisect ALIGN=MIDDLE  ALT=\"bisect\"   DISABLED_style= \"max-width:90%; height:auto;\" > each other. \r<BR>\n" );
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document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB ALIGN=MIDDLE  ALT=\"AB\"   DISABLED_style= \"max-width:90%; height:auto;\" > || <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=CD ALIGN=MIDDLE  ALT=\"CD\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BC ALIGN=MIDDLE  ALT=\"BC\"   DISABLED_style= \"max-width:90%; height:auto;\" > || <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AD ALIGN=MIDDLE  ALT=\"AD\"   DISABLED_style= \"max-width:90%; height:auto;\" >, it’s a parallelogram. Parallel lines have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=same ALIGN=MIDDLE  ALT=\"same\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+slope ALIGN=MIDDLE  ALT=\"+slope\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "So, if slope of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB ALIGN=MIDDLE  ALT=\"AB\"   DISABLED_style= \"max-width:90%; height:auto;\" > = to slope of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=CD ALIGN=MIDDLE  ALT=\"CD\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and slope of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BC ALIGN=MIDDLE  ALT=\"BC\"   DISABLED_style= \"max-width:90%; height:auto;\" > = to slope of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+AD+ ALIGN=MIDDLE  ALT=\"+AD+\"   DISABLED_style= \"max-width:90%; height:auto;\" >then it’s a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=parallelogram ALIGN=MIDDLE  ALT=\"parallelogram\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "slope of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB ALIGN=MIDDLE  ALT=\"AB\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-5-%28-7%29%29%2F%28-3-%28-1%29%29=%28-5%2B7%29%2F%28-3%2B1%29=2%2F-2=-1 ALIGN=MIDDLE  ALT=\"%28-5-%28-7%29%29%2F%28-3-%28-1%29%29=%28-5%2B7%29%2F%28-3%2B1%29=2%2F-2=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "slope of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=CD ALIGN=MIDDLE  ALT=\"CD\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280-2%29%2F%280-%28-2%29%29=-2%2F2=-1 ALIGN=MIDDLE  ALT=\"%280-2%29%2F%280-%28-2%29%29=-2%2F2=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "=>slope of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB+=+CD ALIGN=MIDDLE  ALT=\"AB+=+CD\"   DISABLED_style= \"max-width:90%; height:auto;\" > is same\r<BR>\n" );
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document.write( "slope of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BC+ ALIGN=MIDDLE  ALT=\"BC+\"   DISABLED_style= \"max-width:90%; height:auto;\" >is<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%282-%28-5%29%29%2F%28-2-%28-3%29%29=%282%2B5%29%2F%28-2%2B3%29=7%2F1=7 ALIGN=MIDDLE  ALT=\"+%282-%28-5%29%29%2F%28-2-%28-3%29%29=%282%2B5%29%2F%28-2%2B3%29=7%2F1=7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "slope of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AD ALIGN=MIDDLE  ALT=\"AD\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280-%28-7%29%29%2F%280-%28-1%29%29=7%2F1=7 ALIGN=MIDDLE  ALT=\"%280-%28-7%29%29%2F%280-%28-1%29%29=7%2F1=7\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "=>slope of and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BC+=+AD ALIGN=MIDDLE  ALT=\"BC+=+AD\"   DISABLED_style= \"max-width:90%; height:auto;\" > is same\r<BR>\n" );
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document.write( "hence, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB ALIGN=MIDDLE  ALT=\"AB\"   DISABLED_style= \"max-width:90%; height:auto;\" > || <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=CD ALIGN=MIDDLE  ALT=\"CD\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BC ALIGN=MIDDLE  ALT=\"BC\"   DISABLED_style= \"max-width:90%; height:auto;\" > || <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AD ALIGN=MIDDLE  ALT=\"AD\"   DISABLED_style= \"max-width:90%; height:auto;\" >,=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ABCD ALIGN=MIDDLE  ALT=\"ABCD\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=parallelogram ALIGN=MIDDLE  ALT=\"parallelogram\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "that is enough to prove the diagonals of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ABCD ALIGN=MIDDLE  ALT=\"ABCD\"   DISABLED_style= \"max-width:90%; height:auto;\" > bisect each other\r<BR>\n" );
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document.write( "you can also do it this way:\r<BR>\n" );
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document.write( "find midpoint <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M ALIGN=MIDDLE  ALT=\"M\"   DISABLED_style= \"max-width:90%; height:auto;\" > of diagonals <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AC ALIGN=MIDDLE  ALT=\"AC\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BD ALIGN=MIDDLE  ALT=\"BD\"   DISABLED_style= \"max-width:90%; height:auto;\" >, prove that distances <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AM=MC ALIGN=MIDDLE  ALT=\"AM=MC\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BM=MD ALIGN=MIDDLE  ALT=\"BM=MD\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=change_this_name18480.solver>Finding midpoint of 2 points</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>We use the midpoint formula to solve. The x coordinate is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5B1%5D%2Bx%5B2%5D%29%2F2 ALIGN=MIDDLE  ALT=\"%28x%5B1%5D%2Bx%5B2%5D%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in the values,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%2B-2%29%2F2 ALIGN=MIDDLE  ALT=\"%28-1%2B-2%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F2 ALIGN=MIDDLE  ALT=\"-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >  The x coordinate is -1.5. Now for the y.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-7%2B2%29%2F2 ALIGN=MIDDLE  ALT=\"%28-7%2B2%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5%2F2 ALIGN=MIDDLE  ALT=\"-5%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >  The y coordinate is -2.5. The midpoint is at point (-1.5,-2.5). \r<BR>\n" );
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document.write( "midpoint of diagonal AC:is at point (-1.5,-2.5)\r<BR>\n" );
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document.write( "The distance <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AM=+4.5 ALIGN=MIDDLE  ALT=\"AM=+4.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The distance <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=MC=+4.5 ALIGN=MIDDLE  ALT=\"MC=+4.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=change_this_name18480.solver>Finding midpoint of 2 points</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>We use the midpoint formula to solve. The x coordinate is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5B1%5D%2Bx%5B2%5D%29%2F2 ALIGN=MIDDLE  ALT=\"%28x%5B1%5D%2Bx%5B2%5D%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in the values,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280%2B-3%29%2F2 ALIGN=MIDDLE  ALT=\"%280%2B-3%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F2 ALIGN=MIDDLE  ALT=\"-3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >  The x coordinate is -1.5. Now for the y.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280%2B-5%29%2F2 ALIGN=MIDDLE  ALT=\"%280%2B-5%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5%2F2 ALIGN=MIDDLE  ALT=\"-5%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >  The y coordinate is -2.5. The midpoint is at point (-1.5,-2.5). \r<BR>\n" );
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document.write( "midpoint of diagonal BD: is at point (-1.5,-2.5)\r<BR>\n" );
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document.write( "The distance <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BM=++2.9 ALIGN=MIDDLE  ALT=\"BM=++2.9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The distance <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=MD=++2.9 ALIGN=MIDDLE  ALT=\"MD=++2.9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "check the graph:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing+%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C%0D%0Acircle%28-1%2C-7%2C.12%29%2Ccircle%28-2%2C2%2C.12%29%2Ccircle%28-3%2C-5%2C.12%29%2Ccircle%280%2C0%2C.14%29%2C%0D%0Alocate%28-1%2C-7%2CA%29%2Clocate%28-3%2C-5%2CB%29%2Clocate%28-2%2C2%2CC%29%2Clocate%280.3%2C0.4%2CD%29%2C%0D%0Aline%28-1%2C-7%2C-3%2C-5%29%2Cline%28-1%2C-7%2C0%2C0%29%2Cline%28-2%2C2%2C-3%2C-5%29%2Cline%28-2%2C2%2C0%2C0%29%2C%0D%0Aline%280%2C0%2C-3%2C-5%29%2Cline%28-2%2C2%2C-1%2C-7%29%2Ccircle%28-1.5%2C-2.5%2C.12%29%2Clocate%28-1.5%2C-2.5%2CM%29%2C%0D%0Agraph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C0%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, answer is: the diagonals of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ABCD+ ALIGN=MIDDLE  ALT=\"ABCD+\"   DISABLED_style= \"max-width:90%; height:auto;\" >bisect each other\r<BR>\n" );
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