document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=775986>Question 775986</A>: <I><SPAN STYLE=\"word-break: break-all;\"> for the points (1,4) and (-5,-1) find the distance and the midpoint. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #473284 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=473284\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "the distance:\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 (1, 4), we can say (x1, y1) = (1, 4)<BR>\n" );
document.write( "  So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+1 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D+=+4 ALIGN=MIDDLE  ALT=\"y%5B1%5D+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Since the second point is (-5, -1), we can also say (x2, y2) = (-5, -1)<BR>\n" );
document.write( "  So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+-5 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+-5\"   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" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Put this all together to get:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+1 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D+=+4 ALIGN=MIDDLE  ALT=\"y%5B1%5D+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+-5 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+-5\"   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( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Now use the distance formula to find the distance between the two points (1, 4) and (-5, -1)<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
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" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+sqrt%28%281+-+%28-5%29%29%5E2+%2B+%284+-+%28-1%29%29%5E2%29 ALIGN=MIDDLE  ALT=\"d+=+sqrt%28%281+-+%28-5%29%29%5E2+%2B+%284+-+%28-1%29%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+=+1 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D+=+4 ALIGN=MIDDLE  ALT=\"y%5B1%5D+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+-5 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+-5\"   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" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+sqrt%28%281+%2B+5%29%5E2+%2B+%284+%2B+1%29%5E2%29 ALIGN=MIDDLE  ALT=\"d+=+sqrt%28%281+%2B+5%29%5E2+%2B+%284+%2B+1%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+sqrt%28%286%29%5E2+%2B+%285%29%5E2%29 ALIGN=MIDDLE  ALT=\"d+=+sqrt%28%286%29%5E2+%2B+%285%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+sqrt%2836+%2B+25%29 ALIGN=MIDDLE  ALT=\"d+=+sqrt%2836+%2B+25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+sqrt%2861%29 ALIGN=MIDDLE  ALT=\"d+=+sqrt%2861%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+7.81024967590665 ALIGN=MIDDLE  ALT=\"d+=+7.81024967590665\"   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 (1, 4) and (-5, -1) is exactly <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2861%29 ALIGN=MIDDLE  ALT=\"sqrt%2861%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 7.81024967590665 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%2861%29 ALIGN=MIDDLE  ALT=\"sqrt%2861%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=7.81024967590665 ALIGN=MIDDLE  ALT=\"7.81024967590665\"   DISABLED_style= \"max-width:90%; height:auto;\" > units<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  </TD></TR>\n" );
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document.write( "the midpoint:\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=midpoint.solver>Midpoint</A></TD></TR>\n" );
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document.write( "  <BR>\n" );
document.write( "  The first point is (x1,y1). The second point is (x2,y2)<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Since the first point is (1, 4), we can say (x1, y1) = (1, 4)<BR>\n" );
document.write( "  So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+1 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D+=+4 ALIGN=MIDDLE  ALT=\"y%5B1%5D+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Since the second point is (-5, -1), we can also say (x2, y2) = (-5, -1)<BR>\n" );
document.write( "  So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+-5 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+-5\"   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" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Put this all together to get:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+1 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D+=+4 ALIGN=MIDDLE  ALT=\"y%5B1%5D+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+-5 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+-5\"   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" );
document.write( "  <BR>\n" );
document.write( "  ----------------------------------------------------------------------------------------<BR>\n" );
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document.write( "  <BR>\n" );
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document.write( "  Finding the x coordinate of the midpoint: Add up the corresponding x coordinates x1 and x2 and divide that sum by 2<BR>\n" );
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document.write( "  <BR>\n" );
document.write( "  X Coordinate of Midpoint = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5B1%5D%2Bx%5B2%5D%29%2F2 ALIGN=MIDDLE  ALT=\"%28x%5B1%5D%2Bx%5B2%5D%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  X Coordinate of Midpoint = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2B-5%29%2F2 ALIGN=MIDDLE  ALT=\"%281%2B-5%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  <BR>\n" );
document.write( "  X Coordinate of Midpoint = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2F2 ALIGN=MIDDLE  ALT=\"-4%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  X Coordinate of Midpoint = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
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document.write( "  So the x coordinate of the midpoint is -2<BR>\n" );
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document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Finding the y coordinate of the midpoint: Add up the corresponding y coordinates y1 and y2 and divide that sum by 2<BR>\n" );
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document.write( "  <BR>\n" );
document.write( "  Y Coordinate of Midpoint = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%5B1%5D%2By%5B2%5D%29%2F2 ALIGN=MIDDLE  ALT=\"%28y%5B1%5D%2By%5B2%5D%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Y Coordinate of Midpoint = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2B-1%29%2F2 ALIGN=MIDDLE  ALT=\"%284%2B-1%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Y Coordinate of Midpoint = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F2 ALIGN=MIDDLE  ALT=\"3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  Y Coordinate of Midpoint = <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;\" ><BR>\n" );
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document.write( "  So the y coordinate of the midpoint is 1.5<BR>\n" );
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document.write( "  ===============================================================================<BR>\n" );
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document.write( "  <BR>\n" );
document.write( "  Summary:<BR>\n" );
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document.write( "  The midpoint of the segment joining the two points (1, 4) and (-5, -1) is (-2, 1.5).<BR>\n" );
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document.write( "  So the answer is (-2, 1.5)<BR>\n" );
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document.write( "  </TD></TR>\n" );
document.write( "</TABLE>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );