document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=391317>Question 391317</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Prove that the equation of the perpendicualr bisector of the points (t, t+1) and (3t, t+3) is y +  tx = 2t^2 + t + 2. If this perpendicular bisector passes through the point (5,2), calculate all the possible values of t.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #277727 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=277727\">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( "Determine the slope of the line that passes through <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (t,t\,+\,1)\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (3t,t\,+\,3)\">:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ m\ =\ \frac{t\,+\,1\ -\ (t\,+\,3)}{t\ -\ 3t}\ =  \frac{-2}{-2t}\ =\ \frac{1}{t}\">\r<BR>\n" );
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document.write( "The negative reciprocal of the slope is the slope of the perpendicular, so:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ m_\perp\ =\ -t\">\r<BR>\n" );
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document.write( "Determine the midpoint of the given segment:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ x_m\ = \frac{t + 3t}{2}\ =\ 2t\"> and\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y_m\ = \frac{t\,+\,1\ +\ t\,+\,3}{2}\ =\ t\ +\ 2\">\r<BR>\n" );
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document.write( "Write the desired equation using the point-slope form:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y\ -\ (t\ +\ 2)\ =\ -t(x\ -\ 2t)\">\r<BR>\n" );
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document.write( "Simplify to:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ y\ +\ tx\ =\ 2t^2\ +\ t\ +\ 2\">\r<BR>\n" );
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document.write( "Substitute (5,2) for x and y:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 2\ +\ 5t\ =\ 2t^2\ +\ t\ +\ 2\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 2t^2\ -\ 4t\ =\ 0\">\r<BR>\n" );
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document.write( "Solve the quadratic for the two possible values for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large t\">\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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