document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=490711>Question 490711</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Assignment: \r<BR>\n" );
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document.write( "Proove the points A(6,-13) B(-2,2)  C(13,10) and D (21, -5) are the vertices of the square. Show that the diagonals bisect each other and of equal length. Please have a plan of what you're going to do before proceeding into solving the problem. <BR>\n" );
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document.write( "Hello! How am I going to solve this problem? Am I going to get their distances and midpoints? Please help me. Thank you :) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #334237 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=334237\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First, you can show that AB, BC, CD, and DA are all of equal length. For example,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE AB = \sqrt{(-2 - 6)^2 + (2 - (-13))^2}\">\r<BR>\n" );
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document.write( "However this only proves that the quadrilateral is a rhombus. To prove it is a square, you could perhaps show that one of the angles is 90, then it will follow that the quadrilateral is a square.\r<BR>\n" );
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document.write( "Take the slope of two segments. For example, the slope of line AB is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE m_1 = \frac{2 - (-13)}{-2 - 6} = \frac{15}{-8}\">\r<BR>\n" );
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document.write( "and the slope of BC is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE m_2 = \frac{10 - 2}{13 - (-2)} = \frac{8}{15}\">\r<BR>\n" );
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document.write( "Hence, AB and BC are perpendicular, and it follows that ABCD is a square.\r<BR>\n" );
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