document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=280074>Question 280074</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have two right triangle which are exactly equal and that make a rectangle, if we know three xy coordinates of the the one triangle and all angles how can find unknown xy coordinate of the rectangle </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #203603 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=203603\">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( "<b><i>Read everything before you start doing anything</i></b>\r<BR>\n" );
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document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large A\left(x_1,y_1\right)\"> be the right angle vertex of the given triangle.  Let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large B\left(x_2,y_2\right)\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large C\left(x_3,y_3\right)\">be the other two vertices of the given triangle.  Finally, let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large D\left(x_4,y_4\right)\"> be the unknown point.\r<BR>\n" );
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document.write( "Use the slope formula to calculate the slope of the line containing the segment AB:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ m_{AB}\ =\ \frac{y_1\ -\ y_2}{x_1\ -\ x_2}\">\r<BR>\n" );
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document.write( "Opposite sides of a rectangle are parallel.  Parallel lines have equal slopes.  Using the point-slope form of the equation of a line write an equation of the line parallel to AB that passes through C.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y\ -\ y_3\ =\ m_{AB}(x\ -\ x_3)\">\r<BR>\n" );
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document.write( "Call that result Equation 1.\r<BR>\n" );
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document.write( "Now repeat the entire process, this time computing the slope of the line containing AC and deriving an equation for its parallel through B.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ m_{AC}\ =\ \frac{y_1\ -\ y_3}{x_1\ -\ x_3}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y\ -\ y_2\ =\ m_{AC}(x\ -\ x_2)\">\r<BR>\n" );
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document.write( "And call that Equation 2.\r<BR>\n" );
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document.write( "Finally, solve the system of equations consisting of Equation 1 and Equation 2.  The solution set will be <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large D\left(x_4,y_4\right)\">.\r<BR>\n" );
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document.write( "<b><i>The above is the General solution</i></b>\r<BR>\n" );
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document.write( "If you happen to have a situation where the two legs of your given triangle are parallel to the axes, then the solution is much simpler.  Take the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\">-coordinate of the given point that is on a vertical line above (or below) the unknown point as the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\">-coordinate of the unknown point.  Take the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\">-coordinate of the given point that is on a horizontal line to the right or left of the unknown point as the <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y\">-coordinate of the unknown point.  Done.\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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