document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1067049>Question 1067049</A>: <I><SPAN STYLE=\"word-break: break-all;\"> quadrilateral with midpoints joined<BR>\n" );
document.write( "Quadrilateral ABCD has vertices A(-2,6), B (4,5), C(3,-2), D(-5,1). Points E, F, G, and H are midpoints of the sides of the quadrilateral as shown in the graph. Find the perimeter of quadrilateral EFGH. Round your answer to the nearest tenth. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #682292 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=682292\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If you draw the diagonals,<BR>\n" );
document.write( "you realize that each diagonal<BR>\n" );
document.write( "divides the quadrilatetal into two triangles,<BR>\n" );
document.write( "and the segments connecting the midpoints<BR>\n" );
document.write( "of the sides of ABCD<BR>\n" );
document.write( "are the midsegments of those triangles.<BR>\n" );
document.write( "As such, they are parallel to one or another diagonal,<BR>\n" );
document.write( "and half as long as that diagonal.<BR>\n" );
document.write( "So, the new quadrilateral is a parallelogram,<BR>\n" );
document.write( "and it's perimeter is the sum of the lengths<BR>\n" );
document.write( "of the diagonal of ABCD.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C400%2C-6%2C6%2C-4%2C8%2Cgrid%281%29%2C%0D%0Agreen%28triangle%284%2C5%2C1%2C5.5%2C3.5%2C1.5%29%29%2C%0D%0Agreen%28triangle%283%2C-2%2C3.5%2C1.5%2C-1%2C-0.5%29%29%2C%0D%0Agreen%28triangle%28-5%2C1%2C-1%2C-0.5%2C-3.5%2C3.5%29%29%2C%0D%0Agreen%28triangle%28-2%2C6%2C1%2C5.5%2C-3.5%2C3.5%29%29%2C%0D%0Ared%28line%28-2%2C6%2C4%2C5%29%29%2C%0D%0Ared%28line%284%2C5%2C3%2C-2%29%29%2C%0D%0Ared%28line%283%2C-2%2C-5%2C1%29%29%2C%0D%0Ared%28line%28-5%2C1%2C-2%2C6%29%29%2C%0D%0Agreen%28line%28-2%2C6%2C3%2C-2%29%29%2C%0D%0Agreen%28line%284%2C5%2C-5%2C1%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The lengths of the diagonals are<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AC=sqrt%28%283-%28-2%29%29%5E2%2B%286-%28-2%29%29%5E2%29=sqrt%285%5E2%2B8%5E2%29=sqrt%2825%2B64%29=89 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BD=sqrt%28%284-%28-5%29%29%5E2%2B%285-1%29%5E2%29=sqrt%289%5E2%2B4%5E2%29=sqrt%2881%2B16%29=sqrt%2897%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "so the perimeter of EFGH is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28sqrt%2889%29%2Bsqrt%2897%29%29 ALIGN=MIDDLE  ALT=\"highlight%28sqrt%2889%29%2Bsqrt%2897%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );