document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1124693>Question 1124693</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the equation of the perpendicular bisector of the segment AB, if A(1, �2.5) and B(5, 5.5). If the perpendicular bisector of AB intercepts the y-axis at point P, what are the lengths of PA and PB?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #837917 by </B><A HREF=/tutors/aboutme.mpl?userid=mananth><B>mananth(16946)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mananth><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=mananth><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=837917\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  A(1, -2.5) and B(5, 5.5)\r<BR>\n" );
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document.write( " by mid point formula\r<BR>\n" );
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document.write( "{(x,y) = (x1+x2)/2 , (y1+y2)/2)\r<BR>\n" );
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document.write( "(1+5)/2 , (-2.5+5.5)/2\r<BR>\n" );
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document.write( "mid point of AB  (3,1.5)\r<BR>\n" );
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document.write( "Find the slope of AB\r<BR>\n" );
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document.write( "m = (y1-y2)/(x1-x2)\r<BR>\n" );
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document.write( "(-2.5-5.5)/(1-5)\r<BR>\n" );
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document.write( "=2\r<BR>\n" );
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document.write( "Find the equation of perpendicular to AB\r<BR>\n" );
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document.write( "The slope of perpendicular line will bw negative reciprocal of AB = -1/2\r<BR>\n" );
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document.write( "Equation of perpendicular line \r<BR>\n" );
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document.write( "slope = (-1/2) passing through (3.1.5)\r<BR>\n" );
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document.write( "equation <BR>\n" );
document.write( "y-y1- m(x-x1)  \r<BR>\n" );
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document.write( "y-1.5) = (-1/2) (x-3)\r<BR>\n" );
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document.write( "2y-3= -x+3\r<BR>\n" );
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document.write( "2y+x = 6\r<BR>\n" );
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document.write( "y= 3-(x/2)  equation of perpendicular line to AB\r<BR>\n" );
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document.write( "The line intersects at (0,y)\r<BR>\n" );
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document.write( "Plug x=0\r<BR>\n" );
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document.write( "y=3\r<BR>\n" );
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document.write( "The intersection point on y axis M(0,3) & B\r<BR>\n" );
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document.write( "Distance From (0,3) to B, (5,5.5)\r<BR>\n" );
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document.write( "Use distance formula\r<BR>\n" );
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document.write( "OM = sqrt((5.5-3)^2+(5-0)^2)\r<BR>\n" );
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document.write( "= 5.9 \r<BR>\n" );
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document.write( "Both distances are equal\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/display-illustration.mpl?tutor=mananth&illustration_name=PB.png\">.\r<BR>\n" );
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