document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=618985>Question 618985</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Given: triangle ABC with vertices A(-6,-2), B(2,8), and C(6,-2). Line segment AB has midpoint E, and line segment AC has a midpoint F. Prove: ADEF is a parallelogram and ADEF is NOT a rhombus. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #389284 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=389284\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Point D has to be at (-2,3) or (-4,-7) if indeed ADEF is a parallelogram, and it makes no difference which, the quadrilateral is not a rhombus in either case.\r<BR>\n" );
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document.write( "Use the mid-point formulas to determine the coordinates of point E and F.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x_m\ = \frac{x_1 + x_2}{2}\"> and\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y_m\ = \frac{y_1 + y_2}{2}\">\r<BR>\n" );
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document.write( "I'll leave it to you to verify E(-2,3) and F(0,-2)\r<BR>\n" );
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document.write( "Then using the properties of a parallelogram and the fact that parallel lines have equal slopes, we can determine that point D is either (-2,3) or (-4,-7).\r<BR>\n" );
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document.write( "If ADEF were a rhombus, then either AE = EF or AF = EF (depending on where D is located)\r<BR>\n" );
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document.write( "Use the distance formula to disprove each assertion.  ADEF not a rhombus, Q.E.D\r<BR>\n" );
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document.write( "Distance formula:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ d\ =\ sqrt{(x_1\ -\ x_2)^2\ +\ (y_1\ -\ y_2)^2}\">\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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