document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=980913>Question 980913</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Compute the distance between the two points (1-&#8730;2,-1) and (2+&#8730;2,4). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #601954 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=601954\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <TABLE  BORDER=1>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=distance_formula.solver>Distance Formula</A></TD></TR>\n" );
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document.write( "  The first point is (x1,y1). The second point is (x2,y2)<BR>\n" );
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document.write( "  Since the first point is (-0.414213562373095, -1), we can say (x1, y1) = (-0.414213562373095, -1)<BR>\n" );
document.write( "  So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+-0.414213562373095 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+-0.414213562373095\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D+=+-1 ALIGN=MIDDLE  ALT=\"y%5B1%5D+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  Since the second point is (3.41421356237309, 4), we can also say (x2, y2) = (3.41421356237309, 4)<BR>\n" );
document.write( "  So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+3.41421356237309 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+3.41421356237309\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B2%5D+=+4 ALIGN=MIDDLE  ALT=\"y%5B2%5D+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  Put this all together to get:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+-0.414213562373095 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+-0.414213562373095\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D+=+-1 ALIGN=MIDDLE  ALT=\"y%5B1%5D+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+3.41421356237309 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+3.41421356237309\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B2%5D+=+4 ALIGN=MIDDLE  ALT=\"y%5B2%5D+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  Now use the distance formula to find the distance between the two points (-0.414213562373095, -1) and (3.41421356237309, 4)<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+sqrt%28%28x%5B1%5D-x%5B2%5D%29%5E2+%2B+%28y%5B1%5D+-+y%5B2%5D%29%5E2%29 ALIGN=MIDDLE  ALT=\"d+=+sqrt%28%28x%5B1%5D-x%5B2%5D%29%5E2+%2B+%28y%5B1%5D+-+y%5B2%5D%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+sqrt%28%28-0.414213562373095+-+3.41421356237309%29%5E2+%2B+%28-1+-+4%29%5E2%29 ALIGN=MIDDLE  ALT=\"d+=+sqrt%28%28-0.414213562373095+-+3.41421356237309%29%5E2+%2B+%28-1+-+4%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+-0.414213562373095 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+-0.414213562373095\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D+=+-1 ALIGN=MIDDLE  ALT=\"y%5B1%5D+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+3.41421356237309 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+3.41421356237309\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B2%5D+=+4 ALIGN=MIDDLE  ALT=\"y%5B2%5D+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+sqrt%28%28-3.82842712474618%29%5E2+%2B+%28-5%29%5E2%29 ALIGN=MIDDLE  ALT=\"d+=+sqrt%28%28-3.82842712474618%29%5E2+%2B+%28-5%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+sqrt%2814.6568542494923+%2B+25%29 ALIGN=MIDDLE  ALT=\"d+=+sqrt%2814.6568542494923+%2B+25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+sqrt%2839.6568542494923%29 ALIGN=MIDDLE  ALT=\"d+=+sqrt%2839.6568542494923%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+6.29736883543376 ALIGN=MIDDLE  ALT=\"d+=+6.29736883543376\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  Answer:<BR>\n" );
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document.write( "  The distance between the two points (-0.414213562373095, -1) and (3.41421356237309, 4) is exactly <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2839.6568542494923%29 ALIGN=MIDDLE  ALT=\"sqrt%2839.6568542494923%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > units<BR>\n" );
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document.write( "  The approximate distance between the two points is about 6.29736883543376 units<BR>\n" );
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document.write( "  So again,<BR>\n" );
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document.write( "  Exact Distance: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2839.6568542494923%29 ALIGN=MIDDLE  ALT=\"sqrt%2839.6568542494923%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > units<BR>\n" );
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document.write( "  Approximate Distance: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6.29736883543376 ALIGN=MIDDLE  ALT=\"6.29736883543376\"   DISABLED_style= \"max-width:90%; height:auto;\" > units<BR>\n" );
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