document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203123>Question 1203123</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A quadrilateral has vertices at P (-8, 15), Q (10, 11), R (12, -1), and S (-4, -9)\r<BR>\n" );
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document.write( "a.) What shape is this quadrilateral?\r<BR>\n" );
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document.write( "b.) Do the diagonals bisect each other?\r<BR>\n" );
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document.write( "c.) What shape is formed by connecting the midsegments? (midsegment is a line that connects midpoints)<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 #838437 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=838437\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A quadrilateral has vertices at \r<BR>\n" );
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document.write( "P (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8 ALIGN=MIDDLE  ALT=\"-8\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15 ALIGN=MIDDLE  ALT=\"15\"   DISABLED_style= \"max-width:90%; height:auto;\" >), Q (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10 ALIGN=MIDDLE  ALT=\"10\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11 ALIGN=MIDDLE  ALT=\"11\"   DISABLED_style= \"max-width:90%; height:auto;\" >), R (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12 ALIGN=MIDDLE  ALT=\"12\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-1 ALIGN=MIDDLE  ALT=\"+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >), and S (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4 ALIGN=MIDDLE  ALT=\"-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-9 ALIGN=MIDDLE  ALT=\"-9\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "a.) What shape is this quadrilateral?\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+-20%2C+20%2C+-20%2C+20%2C%0D%0A%0D%0A+circle%28-8%2C15%2C.15%29%2Clocate%28-8%2C16%2CP%29%2C%0D%0Acircle%2810%2C11%2C.15%29%2Clocate%2810%2C12%2CQ%29%2C%0D%0Acircle%2812%2C-1%2C.15%29%2Clocate%2812%2C-2%2CR%29%2C%0D%0Acircle%28-4%2C-9%2C.15%29%2Clocate%28-4%2C-10%2CS%29%2C%0D%0A%0D%0Ablue%28line%28-8%2C15%2C-4%2C-9%29%29%2C%0D%0A%0D%0Ablue%28line%2810%2C11%2C12%2C-1%29%29%2C%0D%0Ablue%28line%28-8%2C15%2C10%2C11%29%29%2C%0D%0A%0D%0Ablue%28line%2812%2C-1%2C-4%2C-9%29%29%2C%0D%0A%0D%0Agraph%28+600%2C+600%2C+-20%2C+20%2C+-20%2C+20%2C+0%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "it could be a trapezoid or a trapezium\r<BR>\n" );
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document.write( " a trapezoid when it has equal angles from a parallel side<BR>\n" );
document.write( "a trapezium  is a quadrilateral with NO parallel sides\r<BR>\n" );
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document.write( "check if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+PS+ ALIGN=MIDDLE  ALT=\"+PS+\"   DISABLED_style= \"max-width:90%; height:auto;\" >and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+QR+ ALIGN=MIDDLE  ALT=\"+QR+\"   DISABLED_style= \"max-width:90%; height:auto;\" >are a pair of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+parallel ALIGN=MIDDLE  ALT=\"+parallel\"   DISABLED_style= \"max-width:90%; height:auto;\" > sides\r<BR>\n" );
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document.write( "Find the slope of the line through the points <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P ALIGN=MIDDLE  ALT=\"+P\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+S ALIGN=MIDDLE  ALT=\"+S\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+Q+ ALIGN=MIDDLE  ALT=\"+Q+\"   DISABLED_style= \"max-width:90%; height:auto;\" >and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+R ALIGN=MIDDLE  ALT=\"+R\"   DISABLED_style= \"max-width:90%; height:auto;\" > as well.\r<BR>\n" );
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document.write( "if slopes are equal, than <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+PS ALIGN=MIDDLE  ALT=\"+PS\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+QR ALIGN=MIDDLE  ALT=\"+QR\"   DISABLED_style= \"max-width:90%; height:auto;\" > are a pair of parallel sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+PS+ ALIGN=MIDDLE  ALT=\"+PS+\"   DISABLED_style= \"max-width:90%; height:auto;\" >slope is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+m=%28y2-y1%29%2F%28x2-x1%29=%28-9-15%29%2F%28-4%2B8%29=-24%2F4=-6 ALIGN=MIDDLE  ALT=\"+m=%28y2-y1%29%2F%28x2-x1%29=%28-9-15%29%2F%28-4%2B8%29=-24%2F4=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+QR ALIGN=MIDDLE  ALT=\"+QR\"   DISABLED_style= \"max-width:90%; height:auto;\" > slope is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+m=%28y2-y1%29%2F%28x2-x1%29=%28-1-11%29%2F%2812-10%29=-12%2F2=-6 ALIGN=MIDDLE  ALT=\"+m=%28y2-y1%29%2F%28x2-x1%29=%28-1-11%29%2F%2812-10%29=-12%2F2=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "slopes are equal => <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=PS ALIGN=MIDDLE  ALT=\"PS\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=QR+ ALIGN=MIDDLE  ALT=\"QR+\"   DISABLED_style= \"max-width:90%; height:auto;\" >are a pair of parallel sides\r<BR>\n" );
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document.write( "so, we have a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=trapezoid+ ALIGN=MIDDLE  ALT=\"trapezoid+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "b.) Do the diagonals bisect each other?\r<BR>\n" );
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document.write( "a trapezoid can have only one pair of parallel sides, means that the diagonals do NOT bisect each other \r<BR>\n" );
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document.write( "c.) What shape is formed by connecting the midsegments? (midsegment is a line that connects midpoints)\r<BR>\n" );
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document.write( "first find midpoints of each side\r<BR>\n" );
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document.write( "P (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8 ALIGN=MIDDLE  ALT=\"-8\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15 ALIGN=MIDDLE  ALT=\"15\"   DISABLED_style= \"max-width:90%; height:auto;\" >), Q (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10 ALIGN=MIDDLE  ALT=\"10\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11 ALIGN=MIDDLE  ALT=\"11\"   DISABLED_style= \"max-width:90%; height:auto;\" >), R (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12 ALIGN=MIDDLE  ALT=\"12\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-1 ALIGN=MIDDLE  ALT=\"+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >), and S (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4 ALIGN=MIDDLE  ALT=\"-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-9 ALIGN=MIDDLE  ALT=\"-9\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "PQ: M1 (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-8%2B10%29%2F2 ALIGN=MIDDLE  ALT=\"%28-8%2B10%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2815%2B11%29%2F2 ALIGN=MIDDLE  ALT=\"%2815%2B11%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)=(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13 ALIGN=MIDDLE  ALT=\"13\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "QR :M2 (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810%2B12%29%2F2 ALIGN=MIDDLE  ALT=\"%2810%2B12%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2811-1%29%2F2 ALIGN=MIDDLE  ALT=\"%2811-1%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)=(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11 ALIGN=MIDDLE  ALT=\"11\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "RS :M3 (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2812-4%29%2F2 ALIGN=MIDDLE  ALT=\"%2812-4%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1-9%29%2F2 ALIGN=MIDDLE  ALT=\"%28-1-9%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)=(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5 ALIGN=MIDDLE  ALT=\"-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "PS:M4  (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-8-4%29%2F2 ALIGN=MIDDLE  ALT=\"%28-8-4%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2815-9%29%2F2 ALIGN=MIDDLE  ALT=\"%2815-9%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >)=(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6 ALIGN=MIDDLE  ALT=\"-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   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=+drawing%28+600%2C+600%2C+-20%2C+20%2C+-20%2C+20%2C%0D%0A%0D%0A+circle%28-8%2C15%2C.15%29%2Clocate%28-8%2C16%2CP%29%2C%0D%0Acircle%2810%2C11%2C.15%29%2Clocate%2810%2C12%2CQ%29%2C%0D%0Acircle%2812%2C-1%2C.15%29%2Clocate%2812%2C-2%2CR%29%2C%0D%0Acircle%28-4%2C-9%2C.15%29%2Clocate%28-4%2C-10%2CS%29%2C%0D%0A%0D%0Ablue%28line%28-8%2C15%2C-4%2C-9%29%29%2C%0D%0A%0D%0Ablue%28line%2810%2C11%2C12%2C-1%29%29%2C%0D%0Ablue%28line%28-8%2C15%2C10%2C11%29%29%2C%0D%0A%0D%0Ablue%28line%2812%2C-1%2C-4%2C-9%29%29%2C%0D%0A%0D%0Acircle%281%2C13%2C.25%29%2Clocate%281%2C13%2CM1%29%2C%0D%0Acircle%2811%2C5%2C.25%29%2Clocate%2811%2C5%2CM2%29%2C%0D%0Acircle%284%2C-5%2C.25%29%2Clocate%284%2C-5%2CM3%29%2C%0D%0Acircle%28-6%2C3%2C.25%29%2Clocate%28-6%2C3%2CM4%29%2C%0D%0Agreen%28line%281%2C13%2C11%2C5%29%29%2C%0D%0Agreen%28line%281%2C13%2C-6%2C3%29%29%2C%0D%0Agreen%28line%2811%2C5%2C4%2C-5%29%29%2C%0D%0Agreen%28line%28-6%2C3%2C4%2C-5%29%29%2C%0D%0A%0D%0Agraph%28+600%2C+600%2C+-20%2C+20%2C+-20%2C+20%2C+0%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "leaving for you to answer what shape is formed by connecting the midsegments\r<BR>\n" );
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