document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=199372>Question 199372</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Analytic Geometry<BR>\n" );
document.write( "14. Use analytic geometry to classify the quadrilateral with vertices D(10,0), E(2,4), F(-8,-6), and G(6,-8). Explain your reasoning and show all your work.\r<BR>\n" );
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document.write( "PLEASE HELP ME!!!<BR>\n" );
document.write( "THANK YOU ALOT!!!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #149815 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=149815\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "Calculate the slopes of the four lines containing the four sides of the quadrilateral using:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ m = \frac{y_1 - y_2}{x_1 - x_2} \">\r<BR>\n" );
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document.write( "where <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(x_1,y_1\right)\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(x_2,y_2\right)\"> are pairs of the given quadrilateral vertices representing the endpoints of the side segments.\r<BR>\n" );
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document.write( "Use:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  L_1 \parallel L_2 \ \ \Leftrightarrow\ \ m_1 = m_2\">\r<BR>\n" );
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document.write( "to determine if any pairs of sides are parallel to each other.\r<BR>\n" );
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document.write( "If you have two sets of parallel sides, then you have some form of parallelogram, either a general parallelogram, a rhombus, a rectangle or a square.\r<BR>\n" );
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document.write( "If you do have a parallelogram, then use:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  L_1 \perp L_2 \ \ \Leftrightarrow\ \ m_1 = -\frac{1}{m_2} \text{ and } m_1, m_2 \neq 0\">\r<BR>\n" );
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document.write( "to determine if the adjacent sides are mutually perpendicular.  If so, then you have a rectangle or a square, if not, a general parallelogram or rhombus.\r<BR>\n" );
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document.write( "At this point you can use the distance formula to determine if two adjacent sides have the same length:\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( "If they do, you have a square or a rhombus based on the perpendicularity determination made above; if not, it is a rectangle or general parallelogram -- again based on perpendicularity.\r<BR>\n" );
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document.write( "If you only have one pair of parallel sides, then you have a trapezoid (trapezium if you are British).\r<BR>\n" );
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document.write( "If you have no pairs of parallel sides, you either have a kite or a general quadrilateral.  A kite has the property that the diagonals are perpendicular.  Use:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ m = \frac{y_1 - y_2}{x_1 - x_2} \">\r<BR>\n" );
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document.write( "on the opposing vertices, namely DF and EG.  Then test for perpendicularity using:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  L_1 \perp L_2 \ \ \Leftrightarrow\ \ m_1 = -\frac{1}{m_2} \text{ and } m_1, m_2 \neq 0\">\r<BR>\n" );
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document.write( "If the diagonals are not perpendicular, you have a general quadrilateral.  If they are perpendicular, you have one additional test to perform.  In a kite, one of the diagonals bisects the other (but not vice versa).\r<BR>\n" );
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document.write( "Use the point-slope form of the equation of a line:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y - y_1 = m(x - x_1) \">\r<BR>\n" );
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document.write( "to write an equation for the lines containing the diagonal segments.\r<BR>\n" );
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document.write( "Solve the system of two equations to determine their point of intersection.  Then use:\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( "to determine the mid-points of each of the diagonal segments.  If one or the other mid-point is the same as the point of intersection of the diagonals, then you have a kite, otherwise it is a general quadrilateral.\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" );
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