document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=951372>Question 951372</A>: <I><SPAN STYLE=\"word-break: break-all;\"> plot the points P (-1,-4) Q ( 1,1) R (4,2) on a coordinate plane. Where should the point S be located  that the figure PQRS  a parallelogram? <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #580993 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=580993\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> P (-1,-4) Q ( 1,1) R (4,2)\r<BR>\n" );
document.write( "\n" );
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%0D%0Acircle%28-1%2C-4%2C.12%29%2Ccircle%281%2C1%2C.12%29%2Ccircle%284%2C2%2C.12%29%2C%0D%0Alocate%28-1%2C-4%2CP%28-1%2C-4%29%29%2Clocate%281%2C1%2CQ%281%2C1%29%29%2Clocate%284%2C2%2CR%284%2C2%29%29%2C%0D%0A+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C0%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "if the figure <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=PQRS ALIGN=MIDDLE  ALT=\"PQRS\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a parallelogram, the point S should be located at intersection point of the line parallel to PQ and the line parallel to SR \r<BR>\n" );
document.write( "\n" );
document.write( "to find the line parallel to PQ , first find a line PQ:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4=m%28-1%29+%2B+b ALIGN=MIDDLE  ALT=\"-4=m%28-1%29+%2B+b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4=-m+%2B+b ALIGN=MIDDLE  ALT=\"-4=-m+%2B+b\"   DISABLED_style= \"max-width:90%; height:auto;\" >...eq.1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1=m+%2B+b ALIGN=MIDDLE  ALT=\"1=m+%2B+b\"   DISABLED_style= \"max-width:90%; height:auto;\" >...eq.2<BR>\n" );
document.write( "-----------------------add<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2B1=-m%2Bm%2Bb+%2B+b ALIGN=MIDDLE  ALT=\"-4%2B1=-m%2Bm%2Bb+%2B+b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3=2b ALIGN=MIDDLE  ALT=\"-3=2b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3%2F2=b ALIGN=MIDDLE  ALT=\"-3%2F2=b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1.5=b ALIGN=MIDDLE  ALT=\"-1.5=b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m ALIGN=MIDDLE  ALT=\"m\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1=m+%2B+b ALIGN=MIDDLE  ALT=\"1=m+%2B+b\"   DISABLED_style= \"max-width:90%; height:auto;\" >...eq.2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1=m+-1.5 ALIGN=MIDDLE  ALT=\"1=m+-1.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2B1.5=m+ ALIGN=MIDDLE  ALT=\"1%2B1.5=m+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.5=m+ ALIGN=MIDDLE  ALT=\"2.5=m+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "the equation of this line is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2.5x-1.5 ALIGN=MIDDLE  ALT=\"y=2.5x-1.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "the line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=SR ALIGN=MIDDLE  ALT=\"SR\"   DISABLED_style= \"max-width:90%; height:auto;\" > has same slope, so:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2.5x+%2B+b ALIGN=MIDDLE  ALT=\"y=2.5x+%2B+b\"   DISABLED_style= \"max-width:90%; height:auto;\" >...since this line passes through  R (4,2), we know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2=2.5%2A4+%2B+b ALIGN=MIDDLE  ALT=\"2=2.5%2A4+%2B+b\"   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=2=10+%2B+b ALIGN=MIDDLE  ALT=\"2=10+%2B+b\"   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=2-10=b ALIGN=MIDDLE  ALT=\"2-10=b\"   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=b=-8 ALIGN=MIDDLE  ALT=\"b=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "the equation of this line is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2.5x-8 ALIGN=MIDDLE  ALT=\"y=2.5x-8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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%28-1%2C-4%2C.12%29%2Ccircle%281%2C1%2C.12%29%2Ccircle%284%2C2%2C.12%29%2C%0D%0Alocate%28-1%2C-4%2CP%28-1%2C-4%29%29%2Clocate%281%2C1%2CQ%281%2C1%29%29%2Clocate%284%2C2%2CR%284%2C2%29%29%2C%0D%0A+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C2.5x+-1.5%2C2.5x-8%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "same way we will find the line SR parallel  to QR<BR>\n" );
document.write( " the line QR: if Q ( 1,1) R (4,2)\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2=m%284%29+%2B+b ALIGN=MIDDLE  ALT=\"2=m%284%29+%2B+b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2=4m+%2B+b ALIGN=MIDDLE  ALT=\"2=4m+%2B+b\"   DISABLED_style= \"max-width:90%; height:auto;\" >...eq.1<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1=m+%2B+b ALIGN=MIDDLE  ALT=\"1=m+%2B+b\"   DISABLED_style= \"max-width:90%; height:auto;\" >...eq.2<BR>\n" );
document.write( "-----------------------subtract\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2-1=4m-m+%2B+b-b ALIGN=MIDDLE  ALT=\"2-1=4m-m+%2B+b-b\"   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=1=3m ALIGN=MIDDLE  ALT=\"1=3m\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=1%2F3 ALIGN=MIDDLE  ALT=\"m=1%2F3\"   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=1=%281%2F3%29+%2B+b ALIGN=MIDDLE  ALT=\"1=%281%2F3%29+%2B+b\"   DISABLED_style= \"max-width:90%; height:auto;\" >...eq.2\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-1%2F3=b ALIGN=MIDDLE  ALT=\"1-1%2F3=b\"   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=b=2%2F3 ALIGN=MIDDLE  ALT=\"b=2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "the equation of this line is:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F3%29x%2B2%2F3 ALIGN=MIDDLE  ALT=\"y=%281%2F3%29x%2B2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "parallel line is:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F3%29x%2Bb ALIGN=MIDDLE  ALT=\"y=%281%2F3%29x%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" > and passes through P (-1,-4)\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4=%281%2F3%29%2A%28-1%29%2Bb ALIGN=MIDDLE  ALT=\"-4=%281%2F3%29%2A%28-1%29%2Bb\"   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=-4=-1%2F3%2Bb ALIGN=MIDDLE  ALT=\"-4=-1%2F3%2Bb\"   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=-4%2B1%2F3=b ALIGN=MIDDLE  ALT=\"-4%2B1%2F3=b\"   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=b=-11%2F3 ALIGN=MIDDLE  ALT=\"b=-11%2F3\"   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=y=%281%2F3%29x-11%2F3 ALIGN=MIDDLE  ALT=\"y=%281%2F3%29x-11%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
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%28-1%2C-4%2C.12%29%2Ccircle%281%2C1%2C.12%29%2Ccircle%284%2C2%2C.12%29%2C%0D%0Alocate%28-1%2C-4%2CP%28-1%2C-4%29%29%2Clocate%281%2C1%2CQ%281%2C1%29%29%2Clocate%284%2C2%2CR%284%2C2%29%29%2C%0D%0A+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C2.5x+-1.5%2C2.5x-8%2C%281%2F3%29x%2B2%2F3%2C%281%2F3%29x-11%2F3%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "intersection of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%281%2F3%29x%2B2%2F3 ALIGN=MIDDLE  ALT=\"y=%281%2F3%29x%2B2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29x-11%2F3 ALIGN=MIDDLE  ALT=\"%281%2F3%29x-11%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the point S\r<BR>\n" );
document.write( "\n" );
document.write( "from the graph, I see the coordinates of the point S are (2,-3)\r<BR>\n" );
document.write( "\n" );
document.write( "check if it is true\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.5x-8=%281%2F3%29x-11%2F3 ALIGN=MIDDLE  ALT=\"2.5x-8=%281%2F3%29x-11%2F3\"   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=7.5x-24=x-11 ALIGN=MIDDLE  ALT=\"7.5x-24=x-11\"   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=7.5x-x=24-11 ALIGN=MIDDLE  ALT=\"7.5x-x=24-11\"   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=6.5x=13 ALIGN=MIDDLE  ALT=\"6.5x=13\"   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=x=13%2F6.5 ALIGN=MIDDLE  ALT=\"x=13%2F6.5\"   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=x=2 ALIGN=MIDDLE  ALT=\"x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2.5%2A2-8=5-8=-3 ALIGN=MIDDLE  ALT=\"y=2.5%2A2-8=5-8=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "so,  the point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S ALIGN=MIDDLE  ALT=\"S\"   DISABLED_style= \"max-width:90%; height:auto;\" > is at  (<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=-3 ALIGN=MIDDLE  ALT=\"-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
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%28-1%2C-4%2C.12%29%2Ccircle%281%2C1%2C.12%29%2Ccircle%284%2C2%2C.12%29%2Ccircle%282%2C-3%2C.12%29%2C%0D%0Alocate%28-1%2C-4%2CP%28-1%2C-4%29%29%2Clocate%281%2C1%2CQ%281%2C1%29%29%2Clocate%284%2C2%2CR%284%2C2%29%29%2Clocate%282%2C-3%2CS%282%2C-3%29%29%2C%0D%0A+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C2.5x+-1.5%2C2.5x-8%2C%281%2F3%29x%2B2%2F3%2C%281%2F3%29x-11%2F3%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );