document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=885998>Question 885998</A>: <I><SPAN STYLE=\"word-break: break-all;\"> P(x,2x)\r<BR>\n" );
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document.write( "The ordinate of a point P is twice the abscissa. This point is equidistant from B(-3,1) and F(8,-2). Find the coordinates of P. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #535612 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=535612\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the point P is equal to (a,b) where b is equal to 2 * a.<BR>\n" );
document.write( "the point P can therefore be represented as (a,2a).\r<BR>\n" );
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document.write( "the point P is equidistant from the points B(-3,1) and F(8,-2)<BR>\n" );
document.write( "this means that the length of the line between P and B is equal to the length of the line between P and F.\r<BR>\n" );
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document.write( "the equation for the length of a line is:<BR>\n" );
document.write( "L = sqrt((x2-x1)^2 + (y2-y1)^2)\r<BR>\n" );
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document.write( "Assign one the points for each line to (x1,y1) and assign the other point for each line to (x2,y2)\r<BR>\n" );
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document.write( "for the first line, you get:<BR>\n" );
document.write( "(x1,y1) = (-3,1)<BR>\n" );
document.write( "(x2,y2) = (a,2a)\r<BR>\n" );
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document.write( "for the second line, you get:<BR>\n" );
document.write( "(x1,y1) = (8,-2)<BR>\n" );
document.write( "(x2,y2) = (a,2a)\r<BR>\n" );
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document.write( "the point (x2,y2) is the point that's common to both lines.\r<BR>\n" );
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document.write( "for each line you want to find the length of the line.\r<BR>\n" );
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document.write( "for the first line, the equation for L becomes:\r<BR>\n" );
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document.write( "L1 = sqrt((a+3)^2 + (2a-1)^2)\r<BR>\n" );
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document.write( "for the second line, the equation for L becomes:\r<BR>\n" );
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document.write( "L2 = sqrt((a-8)^2 + (2a+2)^2)\r<BR>\n" );
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document.write( "simplify both these equations to get:\r<BR>\n" );
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document.write( "L1 = sqrt(2a^2 + 6a + 9 + 4a^2 - 4a + 1)<BR>\n" );
document.write( "L2 = sqrt(2a^2 - 16a + 64 + 4a^2 + 8a + 4)\r<BR>\n" );
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document.write( "simplify these equation further to get:\r<BR>\n" );
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document.write( "L1 = sqrt(6a^2 + 2a + 10)<BR>\n" );
document.write( "L2 = sqrt(6a^2 - 8a + 68)\r<BR>\n" );
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document.write( "set these equations equal to each other to get:\r<BR>\n" );
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document.write( "sqrt(6a^2 + 2a + 10) = sqrt(6a^2 - 8a + 68\r<BR>\n" );
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document.write( "square both sides of this equation to get:\r<BR>\n" );
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document.write( "6a^2 + 2a + 10 = 6a^2 - 8a + 68\r<BR>\n" );
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document.write( "solve for a to get:\r<BR>\n" );
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document.write( "a = 5.8<BR>\n" );
document.write( "2a = 11.6\r<BR>\n" );
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document.write( "those are your solutions for a and 2a and those are the x and y coordinates for point P.\r<BR>\n" );
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document.write( "your 2 lines are:\r<BR>\n" );
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document.write( "L1 = the line between the points (-3,1) and (5.8,11.6)<BR>\n" );
document.write( "L2 = the line between the points (8,-2) and (5.8,11.6)\r<BR>\n" );
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document.write( "to confirm the lengths of these lines are equal, then solve for the lengths of both lines.\r<BR>\n" );
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document.write( "you will find that:\r<BR>\n" );
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document.write( "length of L1 is equal to sqrt(189.8)<BR>\n" );
document.write( "length of L2 is equal to sqrt(189.8)\r<BR>\n" );
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document.write( " </SPAN>\n" );
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