document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=659934>Question 659934</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a quadrilateral has how many vertices o (0,0) p(3,5) Q(8,6) and R(5,1) determine whether OPQR is a parallelogram </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #410994 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=410994\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> vertices O (0,0) P(3,5) Q(8,6) and R(5,1) \r<BR>\n" );
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document.write( "determine whether OPQR is a parallelogram\r<BR>\n" );
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document.write( "first find the distance between given points:\r<BR>\n" );
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document.write( "O (0,0)  R(5,1)\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%285-0%29%5E2+%2B+%281-0%29%5E2%29=+5.09901951359278+ ALIGN=MIDDLE  ALT=\"d=sqrt%28%285-0%29%5E2+%2B+%281-0%29%5E2%29=+5.09901951359278+\"   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( "P(3,5) Q(8,6)\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%283-8%29%5E2+%2B+%285-6%29%5E2%29=+5.09901951359278+ ALIGN=MIDDLE  ALT=\"d=sqrt%28%283-8%29%5E2+%2B+%285-6%29%5E2%29=+5.09901951359278+\"   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( "O (0,0) P(3,5)\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%283-0%29%5E2+%2B+%285-0%29%5E2%29=+5.8309518948453+ ALIGN=MIDDLE  ALT=\"d=sqrt%28%283-0%29%5E2+%2B+%285-0%29%5E2%29=+5.8309518948453+\"   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(5,1) Q(8,6)\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%288-5%29%5E2+%2B+%286-1%29%5E2%29=+5.8309518948453+ ALIGN=MIDDLE  ALT=\"d=sqrt%28%288-5%29%5E2+%2B+%286-1%29%5E2%29=+5.8309518948453+\"   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( "these are equations of the lines through given points:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0.2x+ ALIGN=MIDDLE  ALT=\"y=0.2x+\"   DISABLED_style= \"max-width:90%; height:auto;\" >.........O (0,0)  R(5,1)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0.2x+%2B+4.4 ALIGN=MIDDLE  ALT=\"y=0.2x+%2B+4.4\"   DISABLED_style= \"max-width:90%; height:auto;\" >......P(3,5) Q(8,6)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281.66666666666667%29x+ ALIGN=MIDDLE  ALT=\"y=%281.66666666666667%29x+\"   DISABLED_style= \"max-width:90%; height:auto;\" >............O (0,0) P(3,5)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281.66666666666667%29x+-7.33333333333333 ALIGN=MIDDLE  ALT=\"y=%281.66666666666667%29x+-7.33333333333333\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....R(5,1) Q(8,6)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+%280.2%29x%2C+%280.2%29x+%2B+%284.4%29%2C%281.66666666666667%29x%2C%281.66666666666667%29x+%2B+%28-7.33%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so,  OPQR <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=is ALIGN=MIDDLE  ALT=\"is\"   DISABLED_style= \"max-width:90%; height:auto;\" > a parallelogram\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );