document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=970792>Question 970792</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this :)\r<BR>\n" );
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document.write( "M(5,7), K(x,4), N(4,8) are given. If K is at the same distance from the ponts M and N, then find x </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #593439 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=593439\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> K is a midpoint.\r<BR>\n" );
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document.write( "The distance between M and K is<BR>\n" );
document.write( "sqrt[ (xl-x2)^2 + (y1-y2)^2].  it can also be x2-x1 and y2-y1.  Because it can be squared, it can even be out of order, but I don't recommend doing that.\r<BR>\n" );
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document.write( "In any case the MK distance is sqrt [(5-x)^2 + (7-4)^2}= sqrt (25-10x+x^2 + 9}<BR>\n" );
document.write( "The KN distance is sqrt[(x-4)^2+ (4-8)^2} =sqrt [(x^2-8x+16 +16)= sqrt(x^2 -8x +32)\r<BR>\n" );
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document.write( "These have to equal themselves, and we can remove the radicals.\r<BR>\n" );
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document.write( "x^2-10x +34=x^2 -8x +32\r<BR>\n" );
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document.write( "Subtract x^2 from both sides.\r<BR>\n" );
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document.write( "-10x +34 = -8x +32<BR>\n" );
document.write( "-2x=-2 by adding 8x to both sides and subtracting 34 from both sides\r<BR>\n" );
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document.write( "x=1\r<BR>\n" );
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document.write( "Point is (1,4)\r<BR>\n" );
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document.write( "Check: MK is sqrt (16+9)   point KN is sqrt (9+16)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph+%28300%2C300%2C-5%2C5%2C-2%2C9%2C-x%2B12%29 ALIGN=MIDDLE  ALT=\"+graph+%28300%2C300%2C-5%2C5%2C-2%2C9%2C-x%2B12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This shows the line extended equally in both directions.  Note where (1.4) would be relative to the ends of the line. </SPAN>\n" );
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