document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1045568>Question 1045568</A>: <I><SPAN STYLE=\"word-break: break-all;\"> locate the point which satisfies the given conditions.<BR>\n" );
document.write( "Equidistant from (3,8), (5,2) and (-3,-4)<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 #661038 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=661038\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The point has coordinates x,y<BR>\n" );
document.write( "Distance from (3,8) using distance formula is sqrt[(x-3)^2+(y-8)^2]=[x^2-6x+9+y^2-16y+64]^(1/2)<BR>\n" );
document.write( "Distance from (5,2) is sqrt[(x-5)^2+(y-2)^2]=[x^2-10x+25+y^2-4y+4]^(1/2)<BR>\n" );
document.write( "Distance from (-3,-4) is sqrt ((x+3)^2+(y+4)^2)=[x^2+6x+9+y^2+8y+16}^(1/2)<BR>\n" );
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document.write( "Set the first and third equal to each other, since they are both equidistant.  Then square them, removing the (1/2) exponent.<BR>\n" );
document.write( "[x^2-6x+9+y^2-16y+64]=[x^2+6x+9+y^2+8y+16}<BR>\n" );
document.write( "x^2 and y^2 on both sides cancel<BR>\n" );
document.write( "-6x-16y+73=6x+8y+25<BR>\n" );
document.write( "put x and y on the same side, put the constant on the other side<BR>\n" );
document.write( "48=12x+24y<BR>\n" );
document.write( "divide by 12 to simplify it.<BR>\n" );
document.write( "4=x+2y<BR>\n" );
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document.write( "Now set the first and second equal to each other and square them.<BR>\n" );
document.write( "[x^2-6x+9+y^2-16y+64]=[x^2-10x+25+y^2-4y+4] remove x^2 and y^2<BR>\n" );
document.write( "-6x-16y+73=-10x-4y+29<BR>\n" );
document.write( "44=-4x+12y<BR>\n" );
document.write( "Divide by 4 both sides.<BR>\n" );
document.write( "11=-x+3y<BR>\n" );
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document.write( "4=x+2y<BR>\n" );
document.write( "11=-x+3y<BR>\n" );
document.write( "add them<BR>\n" );
document.write( "15=5y<BR>\n" );
document.write( "y=3<BR>\n" );
document.write( "substitute<BR>\n" );
document.write( "x=-2<BR>\n" );
document.write( "check in the other equation\r<BR>\n" );
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document.write( "(-2,3) ANSWER<BR>\n" );
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document.write( "Distance from (-2,3) to( 3,8), (5,2) and (-3,-4)<BR>\n" );
document.write( "The first is sqrt (25+25), the second is sqrt (49+1) and the third is sqrt (1+49). They are identical.<BR>\n" );
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