document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=972365>Question 972365</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Three friends are planning to visit each other. To optimize travel time, they want the meeting place to be equidistant from the three different cities they live in. The cities are located at A(-16, -1), B(1, 6), and C(1, -18). What are the coordinates where the meeting should take place?\r<BR>\n" );
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document.write( "help me please thank you show work please.:) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #594754 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=594754\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You have 3 lines here:<BR>\n" );
document.write( "AB<BR>\n" );
document.write( "BC<BR>\n" );
document.write( "CA<BR>\n" );
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document.write( "You need to find the equations for the<BR>\n" );
document.write( "perpendicular bisectors of each of these<BR>\n" );
document.write( "lines<BR>\n" );
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document.write( "AB<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+-16+%2B+1+%29+%2F+2+=+-15%2F2+ ALIGN=MIDDLE  ALT=\"+%28+-16+%2B+1+%29+%2F+2+=+-15%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5BAB%5D+=+-15%2F2+ ALIGN=MIDDLE  ALT=\"+x%5BAB%5D+=+-15%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+-1+%2B+6+%29+%2F+2+=+5%2F2+ ALIGN=MIDDLE  ALT=\"+%28+-1+%2B+6+%29+%2F+2+=+5%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y%5BAB%5D+=+5%2F2+ ALIGN=MIDDLE  ALT=\"+y%5BAB%5D+=+5%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So the center of the line AB is<BR>\n" );
document.write( "at ( -15/2 , 5/2 )<BR>\n" );
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document.write( "What's he slope of AB?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+m+=+%28+-1+-+6+%29+%2F+%28+-16+-+1+%29+ ALIGN=MIDDLE  ALT=\"+m+=+%28+-1+-+6+%29+%2F+%28+-16+-+1+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+m+=+7%2F17+ ALIGN=MIDDLE  ALT=\"+m+=+7%2F17+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The slope perpendicular to this is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+m+=+-17%2F7+ ALIGN=MIDDLE  ALT=\"+m+=+-17%2F7+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "Now use point-slope formula:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+y+-+6+%29+%2F+%28+x+-+1+%29+=+-17%2F7+ ALIGN=MIDDLE  ALT=\"+%28+y+-+6+%29+%2F+%28+x+-+1+%29+=+-17%2F7+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+-+6+=+%28-17%2F7%29%2A%28+x+-+1+%29+ ALIGN=MIDDLE  ALT=\"+y+-+6+=+%28-17%2F7%29%2A%28+x+-+1+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+7y+-+42+=+-17x+%2B+17+ ALIGN=MIDDLE  ALT=\"+7y+-+42+=+-17x+%2B+17+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+7y+=+-17x+%2B+59+ ALIGN=MIDDLE  ALT=\"+7y+=+-17x+%2B+59+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=+%28-17%2F7%29%2Ax+%2B+59%2F7+ ALIGN=MIDDLE  ALT=\"+y+=+%28-17%2F7%29%2Ax+%2B+59%2F7+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------------------<BR>\n" );
document.write( "This is the equation of the perpendicular bisector of AB<BR>\n" );
document.write( "( if my math is right )<BR>\n" );
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document.write( "Now do the exact same steps for BC and CA<BR>\n" );
document.write( "The 3 lines you get should meet at the same point.<BR>\n" );
document.write( "( the simultaneous solution ) <BR>\n" );
document.write( "This is the point equidistant from the 3 given points<BR>\n" );
document.write( "Hope this helps\r<BR>\n" );
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