document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1143813>Question 1143813</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given the points A(1,5), B(5,-2) C(-5,-5) and D(-15,1).<BR>\n" );
document.write( "1.Find the area of the quadrilateral ABCD. Hint:divide the area into two triangles.<BR>\n" );
document.write( "2.find the equation  of a line AB?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #764751 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52908)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=764751\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The method to which Alan refers in his post is very robust, &nbsp;but Alan made a number of errors on the way,<BR>\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;so I came to fix it and to get the correct answer/solution.\r<BR>\n" );
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document.write( "Given the points A(1,5), B(5,-2) C(-5,-5) and D(-15,1).<BR>\n" );
document.write( "1.Find the area of the quadrilateral ABCD.<BR>\n" );
document.write( "Here's a better way to do these:<BR>\n" );
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document.write( "     A    B    C    D    A\r\n" );
document.write( "x    1    5   -5   -15   1\r\n" );
document.write( "Y    5   -2   -5    1    5       <----\r\n" );
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document.write( "Add the diagonal products starting at the upper left<BR>\n" );
document.write( "1*(-2) + 5*(-5) + (-5)*1 + (-15)*5 = -2 -25 -5 -75 = -107    &nbsp;&nbsp;&nbsp;&nbsp;<----<BR>\n" );
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document.write( "Add the diagonal products starting at the lower left<BR>\n" );
document.write( "5*5 + (-2)*(-5) + (-5)*(-15) + 1*1 = 25 + 10 + 75 + 1 = 111 &nbsp;&nbsp;&nbsp;&nbsp;<----<BR>\n" );
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document.write( "The difference between the 2 sums is 11 - (-107) = 111 + 107 = 218.                     &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<----<BR>\n" );
document.write( "The area is 1/2 that:   Area = 218/2 = 109 sq units                   &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<----\r<BR>\n" );
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document.write( "<U>Answer for the area</U> :  &nbsp;&nbsp;109 square units.\r<BR>\n" );
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document.write( "By the arrows  &nbsp;\" <---- \"  &nbsp;I showed the lines where I edited Alan's calculations.\r<BR>\n" );
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document.write( "For this method, &nbsp;see the site\r<BR>\n" );
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document.write( "https://www.mathopenref.com/coordpolygonarea.html\r<BR>\n" );
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document.write( "It works for non-convex polygons, &nbsp;too.\r<BR>\n" );
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document.write( "It works, &nbsp;practically, &nbsp;for all and any polygons.\r<BR>\n" );
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document.write( "The major and the only restriction is &nbsp;<U>THIS</U> : &nbsp;&nbsp;a polygon should not have self-intersections.\r<BR>\n" );
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