document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1006745>Question 1006745</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Prove that quadrilateral PLUS with vertices P(2,1), L(6,3), U(5,5), and S(1,3) is a rectangle but not a square </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #622818 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</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=622818\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Prove that quadrilateral <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=PLUS ALIGN=MIDDLE  ALT=\"PLUS\"   DISABLED_style= \"max-width:90%; height:auto;\" > with vertices P(<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=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >), L(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   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;\" >), U(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   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;\" >), and S(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   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;\" >) is a rectangle but not a square\r<BR>\n" );
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document.write( "by definition,a rectangle is a quadrilateral that has opposite sides are parallel and of equal length \r<BR>\n" );
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document.write( "so, we need to find the distance between vertices which is the length of the sides\r<BR>\n" );
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document.write( "if the distance between points <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P ALIGN=MIDDLE  ALT=\"P\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L ALIGN=MIDDLE  ALT=\"L\"   DISABLED_style= \"max-width:90%; height:auto;\" > is same as the distance between points <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=U ALIGN=MIDDLE  ALT=\"U\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S ALIGN=MIDDLE  ALT=\"S\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then the length of the sides <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=PL ALIGN=MIDDLE  ALT=\"PL\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=US ALIGN=MIDDLE  ALT=\"US\"   DISABLED_style= \"max-width:90%; height:auto;\" > are same, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=PL=US ALIGN=MIDDLE  ALT=\"PL=US\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and if the distance between points <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=U ALIGN=MIDDLE  ALT=\"U\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L ALIGN=MIDDLE  ALT=\"L\"   DISABLED_style= \"max-width:90%; height:auto;\" > is same as the distance between points <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P ALIGN=MIDDLE  ALT=\"P\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S ALIGN=MIDDLE  ALT=\"S\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then the length of the sides <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=UL ALIGN=MIDDLE  ALT=\"UL\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=PS ALIGN=MIDDLE  ALT=\"PS\"   DISABLED_style= \"max-width:90%; height:auto;\" > are same, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=UL=PS ALIGN=MIDDLE  ALT=\"UL=PS\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "finally, if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=PL%3C%3EPS ALIGN=MIDDLE  ALT=\"PL%3C%3EPS\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=US%3C%3EUL ALIGN=MIDDLE  ALT=\"US%3C%3EUL\"   DISABLED_style= \"max-width:90%; height:auto;\" >then a quadrilateral is a rectangle\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=PL ALIGN=MIDDLE  ALT=\"PL\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<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_for_Coordinate_Plane.solver>Distance Formula to determine length on coordinate plane</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>The distance (d) between two points is given by the following formula:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=sqrt%28%28x2-x1%29%5E2+%2B+%28y2-y1%29%5E2%29 ALIGN=MIDDLE  ALT=\"d=sqrt%28%28x2-x1%29%5E2+%2B+%28y2-y1%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Thus in our case, the required distance is<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=sqrt%28%286-2%29%5E2+%2B+%283-1%29%5E2%29=+4.47213595499958+ ALIGN=MIDDLE  ALT=\"d=sqrt%28%286-2%29%5E2+%2B+%283-1%29%5E2%29=+4.47213595499958+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For more on this concept, refer to <A  rel=nofollow HREF=Distance_formula.wikipedia>Distance formula</A>.<BR>\n" );
document.write( "  </TD></TR>\n" );
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document.write( " \r<BR>\n" );
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document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=US ALIGN=MIDDLE  ALT=\"US\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<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_for_Coordinate_Plane.solver>Distance Formula to determine length on coordinate plane</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>The distance (d) between two points is given by the following formula:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=sqrt%28%28x2-x1%29%5E2+%2B+%28y2-y1%29%5E2%29 ALIGN=MIDDLE  ALT=\"d=sqrt%28%28x2-x1%29%5E2+%2B+%28y2-y1%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Thus in our case, the required distance is<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=sqrt%28%281-5%29%5E2+%2B+%283-5%29%5E2%29=+4.47213595499958+ ALIGN=MIDDLE  ALT=\"d=sqrt%28%281-5%29%5E2+%2B+%283-5%29%5E2%29=+4.47213595499958+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For more on this concept, refer to <A  rel=nofollow HREF=Distance_formula.wikipedia>Distance formula</A>.<BR>\n" );
document.write( "  </TD></TR>\n" );
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document.write( " \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=UL ALIGN=MIDDLE  ALT=\"UL\"   DISABLED_style= \"max-width:90%; height:auto;\" > <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_for_Coordinate_Plane.solver>Distance Formula to determine length on coordinate plane</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>The distance (d) between two points is given by the following formula:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=sqrt%28%28x2-x1%29%5E2+%2B+%28y2-y1%29%5E2%29 ALIGN=MIDDLE  ALT=\"d=sqrt%28%28x2-x1%29%5E2+%2B+%28y2-y1%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Thus in our case, the required distance is<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=sqrt%28%286-5%29%5E2+%2B+%283-5%29%5E2%29=+2.23606797749979+ ALIGN=MIDDLE  ALT=\"d=sqrt%28%286-5%29%5E2+%2B+%283-5%29%5E2%29=+2.23606797749979+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For more on this concept, refer to <A  rel=nofollow HREF=Distance_formula.wikipedia>Distance formula</A>.<BR>\n" );
document.write( "  </TD></TR>\n" );
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document.write( " <BR>\n" );
document.write( "and \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=PS ALIGN=MIDDLE  ALT=\"PS\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
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_for_Coordinate_Plane.solver>Distance Formula to determine length on coordinate plane</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>The distance (d) between two points is given by the following formula:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=sqrt%28%28x2-x1%29%5E2+%2B+%28y2-y1%29%5E2%29 ALIGN=MIDDLE  ALT=\"d=sqrt%28%28x2-x1%29%5E2+%2B+%28y2-y1%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Thus in our case, the required distance is<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=sqrt%28%281-2%29%5E2+%2B+%283-1%29%5E2%29=+2.23606797749979+ ALIGN=MIDDLE  ALT=\"d=sqrt%28%281-2%29%5E2+%2B+%283-1%29%5E2%29=+2.23606797749979+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For more on this concept, refer to <A  rel=nofollow HREF=Distance_formula.wikipedia>Distance formula</A>.<BR>\n" );
document.write( "  </TD></TR>\n" );
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document.write( " \r<BR>\n" );
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document.write( "as you can see, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=PL=US ALIGN=MIDDLE  ALT=\"PL=US\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=UL=PS ALIGN=MIDDLE  ALT=\"UL=PS\"   DISABLED_style= \"max-width:90%; height:auto;\" >;so, a quadrilateral is a rectangle\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%0Acircle%282%2C1%2C.12%29%2Ccircle%286%2C3%2C.12%29%2Ccircle%285%2C5%2C.12%29%2Ccircle%281%2C3%2C.12%29%2C%0D%0Alocate%282%2C1%2CP%29%2Clocate%286%2C3%2CL%29%2Clocate%285%2C5%2CU%29%2Clocate%281%2C3%2CS%29%2C%0D%0Aline%282%2C1%2C1%2C3%29%2Cline%285%2C5%2C1%2C3%29%2Cline%286%2C3%2C2%2C1%29%2Cline%285%2C5%2C6%2C3%29%2C%0D%0A+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+0%29%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" );