document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=779326>Question 779326</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given the endpoints of a diameter of a circle at (4,1) and (-4,-4), find the center and radius of the circle.  Write its equation in  standard form.\r<BR>\n" );
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document.write( "Thanks in advance for your help. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #475205 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=475205\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if the endpoints of a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=diameter ALIGN=MIDDLE  ALT=\"diameter\"   DISABLED_style= \"max-width:90%; height:auto;\" > of a circle at (4,1) and (-4,-4), then the center is midpoint:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > coordinate of midpoint is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x1%2Bx2%29%2F2=%284%2B%28-4%29%29%2F2=0%2F2=0 ALIGN=MIDDLE  ALT=\"%28x1%2Bx2%29%2F2=%284%2B%28-4%29%29%2F2=0%2F2=0\"   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=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > coordinate of midpoint is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y1%2By2%29%2F2=%281%2B%28-4%29%29%2F2=-3%2F2=-1.5 ALIGN=MIDDLE  ALT=\"%28y1%2By2%29%2F2=%281%2B%28-4%29%29%2F2=-3%2F2=-1.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, the center is at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1.5 ALIGN=MIDDLE  ALT=\"-1.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and it means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=0 ALIGN=MIDDLE  ALT=\"h=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=-1.5 ALIGN=MIDDLE  ALT=\"k=-1.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "now find the length of radius which is equal to distance between one endpoint and midpoint of diameter\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 (0, -1.5), we can say (x1, y1) = (0, -1.5)<BR>\n" );
document.write( "  So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+0 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D+=+-1.5 ALIGN=MIDDLE  ALT=\"y%5B1%5D+=+-1.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  Since the second point is (4, 1), we can also say (x2, y2) = (4, 1)<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+=+1 ALIGN=MIDDLE  ALT=\"y%5B2%5D+=+1\"   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 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D+=+-1.5 ALIGN=MIDDLE  ALT=\"y%5B1%5D+=+-1.5\"   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+=+1 ALIGN=MIDDLE  ALT=\"y%5B2%5D+=+1\"   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, -1.5) and (4, 1)<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%280+-+4%29%5E2+%2B+%28-1.5+-+1%29%5E2%29 ALIGN=MIDDLE  ALT=\"d+=+sqrt%28%280+-+4%29%5E2+%2B+%28-1.5+-+1%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 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D+=+-1.5 ALIGN=MIDDLE  ALT=\"y%5B1%5D+=+-1.5\"   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+=+1 ALIGN=MIDDLE  ALT=\"y%5B2%5D+=+1\"   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%28-4%29%5E2+%2B+%28-2.5%29%5E2%29 ALIGN=MIDDLE  ALT=\"d+=+sqrt%28%28-4%29%5E2+%2B+%28-2.5%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%2816+%2B+6.25%29 ALIGN=MIDDLE  ALT=\"d+=+sqrt%2816+%2B+6.25%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%2822.25%29 ALIGN=MIDDLE  ALT=\"d+=+sqrt%2822.25%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+=+4.7169905660283 ALIGN=MIDDLE  ALT=\"d+=+4.7169905660283\"   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, -1.5) and (4, 1) is exactly <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2822.25%29 ALIGN=MIDDLE  ALT=\"sqrt%2822.25%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 4.7169905660283 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%2822.25%29 ALIGN=MIDDLE  ALT=\"sqrt%2822.25%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=4.7169905660283 ALIGN=MIDDLE  ALT=\"4.7169905660283\"   DISABLED_style= \"max-width:90%; height:auto;\" > units<BR>\n" );
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document.write( " \r<BR>\n" );
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document.write( "so, radius is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=4.72 ALIGN=MIDDLE  ALT=\"r=4.72\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "equation of a circle in  standard form: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-h%29%5E2+%2B+%28y-k%29%5E2+=+r%5E2 ALIGN=MIDDLE  ALT=\"%28x+-h%29%5E2+%2B+%28y-k%29%5E2+=+r%5E2\"   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=%28x+-0%29%5E2+%2B+%28y-%28-1.5%29%29%5E2+=+%284.72%29%5E2 ALIGN=MIDDLE  ALT=\"%28x+-0%29%5E2+%2B+%28y-%28-1.5%29%29%5E2+=+%284.72%29%5E2\"   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=x%5E2+%2B+%28y%2B1.5%29%5E2+=+22.28 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+%28y%2B1.5%29%5E2+=+22.28\"   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=drawing%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C%0D%0A++grid%28+1+%29%2Clocate%280%2C-1.5%2CC%280%2C-1.5%29%29%2Clocate%284%2C1%2CA%284%2C1%29%29%2Clocate%28-4%2C-4%2CB%28-4%2C-4%29%29%2C%0D%0A++blue%28circle%28+0%2C+-1.5%2C4.72+%29%29%2C%0D%0A++%0D%0A++line%28+-4%2C+-4%2C+4%2C+1+%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );