document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=29436>Question 29436</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Problem states: \"Let P=(x,y) be a point on the graph of y= square root of x. Express the distance \"d\" from point P to the point (1,0) as a function of x.\"<BR>\n" );
document.write( "I get to \"square root of (x-1)^ + y^\", then I'm confused. Please help </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #16259 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=16259\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you are along the right lines but you have missed one crucial \"leap of insight\".\r<BR>\n" );
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document.write( "at any point on the curve, the x-value is x but the y-value is not just y...it is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "So, the distance between A(1,0) and P(x,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >) is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+AP+=+sqrt%28%28x-1%29%5E2+%2B+%28sqrt%28x%29-0%29%5E2%29+ ALIGN=MIDDLE  ALT=\"+AP+=+sqrt%28%28x-1%29%5E2+%2B+%28sqrt%28x%29-0%29%5E2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+AP+=+sqrt%28%28x%5E2-2x%2B1%29+%2B+%28sqrt%28x%29%29%5E2%29+ ALIGN=MIDDLE  ALT=\"+AP+=+sqrt%28%28x%5E2-2x%2B1%29+%2B+%28sqrt%28x%29%29%5E2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+AP+=+sqrt%28%28x%5E2-2x%2B1%29+%2B+x+%29+ ALIGN=MIDDLE  ALT=\"+AP+=+sqrt%28%28x%5E2-2x%2B1%29+%2B+x+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+AP+=+sqrt%28%28x%5E2-x%2B1%29+%29+ ALIGN=MIDDLE  ALT=\"+AP+=+sqrt%28%28x%5E2-x%2B1%29+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "this is the answer.\r<BR>\n" );
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document.write( "CHECK:<BR>\n" );
document.write( "If P(0,0), the length of AP should be 1.<BR>\n" );
document.write( "--> put x=0 into the formula and we get 1.\r<BR>\n" );
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document.write( "Pick say P(25,5), then from coordinate geometry, AP = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28601%29 ALIGN=MIDDLE  ALT=\"sqrt%28601%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Putting x=25 into the formula gives us this.\r<BR>\n" );
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document.write( "jon.<BR>\n" );
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