document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=946623>Question 946623</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the area and perimeter of a polygon with vertices A(1,2), B(2,-1), C(-1,-2), D(-2,1)  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #577530 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=577530\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A(1,2), B(2,-1), C(-1,-2), D(-2,1) \r<BR>\n" );
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document.write( "first draw a polygon using given vertices:\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%281%2C2%2C.12%29%2C+circle%282%2C-1%2C.12%29%2Ccircle%28-1%2C-2%2C.12%29%2C+circle%28-2%2C1%2C.12%29%2C%0D%0A%0D%0Alocate%281%2C2%2CA%281%2C2%29%29%2C+locate%282%2C-1%2CB%282%2C-1%29%29%2C%0D%0A%0D%0Alocate%28-1%2C-2%2CC%28-1%2C-2%29%29%2C+locate%28-2%2C1%2CD%28-2%2C1%29%29%2C%0D%0A%0D%0Ablue%28line%281%2C2%2C2%2C-1%29%29%2C+blue%28line%281%2C2%2C-2%2C1%29%29%2C%0D%0Ablue%28line%282%2C-1%2C-1%2C-2%29%29%2C+blue%28line%28-2%2C1%2C-1%2C-2%29%29%2C%0D%0Agraph%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( "find distance <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AB%7D%2C%7B%7B%7BAD%7D%2C%7B%7B%7BCD ALIGN=MIDDLE  ALT=\"AB%7D%2C%7B%7B%7BAD%7D%2C%7B%7B%7BCD\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BC%7D%3A%0D%0A%0D%0AA%281%2C2%29%2C+B%282%2C-1%29%2C+C%28-1%2C-2%29%2C+D%28-2%2C1%29+%0D%0A%0D%0A%3CTABLE+BORDER=1%3E%0A+%3CTR%3E%3CTD+ALIGN=MIDDLE%3ESolved+by+%3CA+ rel=nofollow HREF=http%3A%2F%2Fwiki.algebra.com%2Findex.php%2FTutoring_-_pluggable_solvers%3Epluggable%3C%2FA%3E+solver%3A+%3CA+ rel=nofollow HREF=Distance_Formula_for_Coordinate_Plane.solver%3EDistance+Formula+to+determine+length+on+coordinate+plane%3C%2FA%3E%3C%2FTD%3E%3C%2FTR%3E%0A%3CTR%3E%3CTD+ALIGN=LEFT%3EThe+distance+%28d%29+between+two+points+is+given+by+the+following+formula%3A%0D%0A++%0D%0A++%7B%7B%7Bd=sqrt%28%28x2-x1%29%5E2+%2B+%28y2-y1%29%5E2%29 ALIGN=MIDDLE   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%282-1%29%5E2+%2B+%28-1-2%29%5E2%29=+3.16227766016838+ ALIGN=MIDDLE  ALT=\"d=sqrt%28%282-1%29%5E2+%2B+%28-1-2%29%5E2%29=+3.16227766016838+\"   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></TABLE>\n" );
document.write( " \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AD%7D%0D%0A%3CTABLE+BORDER=1%3E%0A+%3CTR%3E%3CTD+ALIGN=MIDDLE%3ESolved+by+%3CA+ rel=nofollow HREF=http%3A%2F%2Fwiki.algebra.com%2Findex.php%2FTutoring_-_pluggable_solvers%3Epluggable%3C%2FA%3E+solver%3A+%3CA+ rel=nofollow HREF=Distance_Formula_for_Coordinate_Plane.solver%3EDistance+Formula+to+determine+length+on+coordinate+plane%3C%2FA%3E%3C%2FTD%3E%3C%2FTR%3E%0A%3CTR%3E%3CTD+ALIGN=LEFT%3EThe+distance+%28d%29+between+two+points+is+given+by+the+following+formula%3A%0D%0A++%0D%0A++%7B%7B%7Bd=sqrt%28%28x2-x1%29%5E2+%2B+%28y2-y1%29%5E2%29 ALIGN=MIDDLE   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%28-2-1%29%5E2+%2B+%281-2%29%5E2%29=+3.16227766016838+ ALIGN=MIDDLE  ALT=\"d=sqrt%28%28-2-1%29%5E2+%2B+%281-2%29%5E2%29=+3.16227766016838+\"   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></TABLE>\n" );
document.write( " \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=CD ALIGN=MIDDLE  ALT=\"CD\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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%28-2--1%29%5E2+%2B+%281--2%29%5E2%29=+3.16227766016838+ ALIGN=MIDDLE  ALT=\"d=sqrt%28%28-2--1%29%5E2+%2B+%281--2%29%5E2%29=+3.16227766016838+\"   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" );
document.write( "</TABLE>\n" );
document.write( " \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BC%7D%0D%0A%3CTABLE+BORDER=1%3E%0A+%3CTR%3E%3CTD+ALIGN=MIDDLE%3ESolved+by+%3CA+ rel=nofollow HREF=http%3A%2F%2Fwiki.algebra.com%2Findex.php%2FTutoring_-_pluggable_solvers%3Epluggable%3C%2FA%3E+solver%3A+%3CA+ rel=nofollow HREF=Distance_Formula_for_Coordinate_Plane.solver%3EDistance+Formula+to+determine+length+on+coordinate+plane%3C%2FA%3E%3C%2FTD%3E%3C%2FTR%3E%0A%3CTR%3E%3CTD+ALIGN=LEFT%3EThe+distance+%28d%29+between+two+points+is+given+by+the+following+formula%3A%0D%0A++%0D%0A++%7B%7B%7Bd=sqrt%28%28x2-x1%29%5E2+%2B+%28y2-y1%29%5E2%29 ALIGN=MIDDLE   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%282--1%29%5E2+%2B+%28-1--2%29%5E2%29=+3.16227766016838+ ALIGN=MIDDLE  ALT=\"d=sqrt%28%282--1%29%5E2+%2B+%28-1--2%29%5E2%29=+3.16227766016838+\"   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></TABLE>\n" );
document.write( " \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " since all distances same => your polygon is a square and the length of its side is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=3.16227766016838 ALIGN=MIDDLE  ALT=\"a=3.16227766016838\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "then the area and perimeter of this polygon will be:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=a%5E2 ALIGN=MIDDLE  ALT=\"A=a%5E2\"   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=A=%283.16227766016838%29%5E2 ALIGN=MIDDLE  ALT=\"A=%283.16227766016838%29%5E2\"   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=A=10 ALIGN=MIDDLE  ALT=\"A=10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "perimeter:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=4a ALIGN=MIDDLE  ALT=\"P=4a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=4%2A3.16227766016838 ALIGN=MIDDLE  ALT=\"P=4%2A3.16227766016838\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=12.64911064067352 ALIGN=MIDDLE  ALT=\"P=12.64911064067352\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=12.65 ALIGN=MIDDLE  ALT=\"P=12.65\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );