document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1042721>Question 1042721</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two cities are located in the xy-plane at the points A(7, 5) and B 3(13, 8). A company wishes to place a factory on a road between the cities at A and B. It is determined that the company can make the most money if it places the factory exactly halfway between\r<BR>\n" );
document.write( "\n" );
document.write( "A and B. However, due to environmental hazards produced by the factory, it is safe for the people living in City A and City B only if the factory is located exactly one third of the distance from City A going toward City B.<BR>\n" );
document.write( "Find the coordinates of the point where the factory should be placed to ensure the most ethical outcome.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #657748 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=657748\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \"Most ethical outcome\" and \"safest....one third of the dis...from A to B\", means find the  the point one third of the distance from A to B.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Unknown point (x,y).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28x-7%29%5E2%2B%28y-5%29%5E2%29%2Fsqrt%28%2813-7%29%5E2%2B%288-5%29%5E2%29=1%2F3 ALIGN=MIDDLE  ALT=\"sqrt%28%28x-7%29%5E2%2B%28y-5%29%5E2%29%2Fsqrt%28%2813-7%29%5E2%2B%288-5%29%5E2%29=1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Asqrt%28%28x-7%29%5E2%2B%28y-5%29%5E2%29=sqrt%2825%2B9%29 ALIGN=MIDDLE  ALT=\"3%2Asqrt%28%28x-7%29%5E2%2B%28y-5%29%5E2%29=sqrt%2825%2B9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28x-7%29%5E2%2B%28y-5%29%5E2%29=12 ALIGN=MIDDLE  ALT=\"sqrt%28%28x-7%29%5E2%2B%28y-5%29%5E2%29=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Before continuing with this somewhat simplified equation, find the equation in slope-intercept form for the line containing A and B.  Substitute for y in the radical equation above.  Continue to solve first for x. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );