document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=955158>Question 955158</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the circumference of a circle with center A(2,3) and passes through B(4,5)? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #583430 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=583430\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the circumference of a circle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=2r%2Api ALIGN=MIDDLE  ALT=\"C=2r%2Api\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " a circle with center A(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and passes through B(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" >) will have a radius <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" > equal to distance between points A and B\r<BR>\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 (2, 3), we can say (x1, y1) = (2, 3)<BR>\n" );
document.write( "  So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+2 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D+=+3 ALIGN=MIDDLE  ALT=\"y%5B1%5D+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  Since the second point is (4, 5), we can also say (x2, y2) = (4, 5)<BR>\n" );
document.write( "  So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+4 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B2%5D+=+5 ALIGN=MIDDLE  ALT=\"y%5B2%5D+=+5\"   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+=+2 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D+=+3 ALIGN=MIDDLE  ALT=\"y%5B1%5D+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+4 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B2%5D+=+5 ALIGN=MIDDLE  ALT=\"y%5B2%5D+=+5\"   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 (2, 3) and (4, 5)<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%282+-+4%29%5E2+%2B+%283+-+5%29%5E2%29 ALIGN=MIDDLE  ALT=\"d+=+sqrt%28%282+-+4%29%5E2+%2B+%283+-+5%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+=+2 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D+=+3 ALIGN=MIDDLE  ALT=\"y%5B1%5D+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+4 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B2%5D+=+5 ALIGN=MIDDLE  ALT=\"y%5B2%5D+=+5\"   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%28-2%29%5E2+%2B+%28-2%29%5E2%29 ALIGN=MIDDLE  ALT=\"d+=+sqrt%28%28-2%29%5E2+%2B+%28-2%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%284+%2B+4%29 ALIGN=MIDDLE  ALT=\"d+=+sqrt%284+%2B+4%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%288%29 ALIGN=MIDDLE  ALT=\"d+=+sqrt%288%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <br><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+sqrt%284%2A2%29 ALIGN=MIDDLE  ALT=\"d+=+sqrt%284%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><br><br><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+sqrt%284%29%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"d+=+sqrt%284%29%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><br><br><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+2%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"d+=+2%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><br><BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+2.82842712474619 ALIGN=MIDDLE  ALT=\"d+=+2.82842712474619\"   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 (2, 3) and (4, 5) is exactly <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"2%2Asqrt%282%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 2.82842712474619 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=2%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"2%2Asqrt%282%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=2.82842712474619 ALIGN=MIDDLE  ALT=\"2.82842712474619\"   DISABLED_style= \"max-width:90%; height:auto;\" > units<BR>\n" );
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document.write( "  </TD></TR>\n" );
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document.write( "so, if we use the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=2sqrt%282%29 ALIGN=MIDDLE  ALT=\"d=2sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=2r%2Api ALIGN=MIDDLE  ALT=\"C=2r%2Api\"   DISABLED_style= \"max-width:90%; height:auto;\" > will be\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=2%2A2sqrt%282%29%2Api ALIGN=MIDDLE  ALT=\"C=2%2A2sqrt%282%29%2Api\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=4sqrt%282%29%2Api ALIGN=MIDDLE  ALT=\"C=4sqrt%282%29%2Api\"   DISABLED_style= \"max-width:90%; height:auto;\" > or as decimal\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=4%2A2.83%2A3.14 ALIGN=MIDDLE  ALT=\"C=4%2A2.83%2A3.14\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=35.5448 ALIGN=MIDDLE  ALT=\"C=35.5448\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=35.51 ALIGN=MIDDLE  ALT=\"C=35.51\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%0D%0Acircle%282%2C3%2C.12%29%2Ccircle%284%2C5%2C.12%29%2Ccircle%282%2C3%2C2sqrt%282%29%29%2C%0D%0Alocate%282%2C3%2CA%282%2C3%29%29%2Clocate%284%2C5%2CB%284%2C5%29%29%2C%0D%0Aline%282%2C3%2C4%2C5%29%2C+locate%282.5%2C4.5%2Cr%282sqrt%282%29%29%29%2C%0D%0A+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C0+%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );