document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=184086>Question 184086</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find an equation y = m x + b of the perpendicular bisector of the line segment joining the points A(3,5) and B(9,-1).<BR>\n" );
document.write( "The slope m is<BR>\n" );
document.write( "The constant b is  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #138137 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=138137\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "First thing to do is find the coordinates of the mid-point of line segment <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \overline{AB}\">.  That is because the perpendicular bisector of the line segment intersects the line segment at the mid-point by definition of a perpendicular bisector.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Use the mid-point formula:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math (x_m,y_m) = \left(\frac{x_1 - x_2}{2},\frac{y_1 - y_2}{2}\right)\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "where <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (x_1,y_1)\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (x_2,y_2)\"> are the endpoints of the line segment.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Next you need the slope, <i>m</i>, of the line that contains the line segment:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math m = \frac{y_1 - y_2}{x_1 - x_2}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "where <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (x_1,y_1)\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (x_2,y_2)\"> are the endpoints of the line segment.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The slope of a perpendicular is the negative reciprocal of the slope of the given line, that is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math L_1 \perp L_2 \ \ \Leftrightarrow\ \ m_1 = -\frac{1}{m_2}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So, calculate <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large -\frac{1}{m}\"> using the value of the slope, <i>m</i>, determined above.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Then use this new slope value plus the fact that the calculated midpoint, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (x_m,y_m)\"> is a point on the desired perpendicular to provide the given information for the point-slope form of the equation of a straight line, namely:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \text{          }\math y - y_m = -\frac{1}{m}(x - x_m)\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Make the appropriate substitutions for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large (x_m,y_m)\"> and <i>m</i> and then solve the equation for <i>y</i> in terms of <i>x</i> to obtain the desired slope-intercept form, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large y = m_p x + b\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The resulting <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large m_p\"> and <i>b</i> will be the answers requested.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
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( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );