document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=935864>Question 935864</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine the equation of the line on which the side of a given rhombus lie if the 3 other sides lie on 3x +2y + 12 =0, 4x -3y -12=0 and 6x +4y -11=0.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #569220 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=569220\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If a parallelogram has two consecutive sides <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=congruent ALIGN=MIDDLE  ALT=\"congruent\"   DISABLED_style= \"max-width:90%; height:auto;\" >, it is a rhombus. Also oppo \r<BR>\n" );
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document.write( "if the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > other sides lie on <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x+%2B2y+%2B+12+=0 ALIGN=MIDDLE  ALT=\"3x+%2B2y+%2B+12+=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4x+-3y+-12=0 ALIGN=MIDDLE  ALT=\"+4x+-3y+-12=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x+%2B4y+-11=0 ALIGN=MIDDLE  ALT=\"6x+%2B4y+-11=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then fourth side lie on <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%2Bby%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%2Bby%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "write these lines in slope-intercept form<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x+%2B2y+%2B+12+=0 ALIGN=MIDDLE  ALT=\"3x+%2B2y+%2B+12+=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=-%283%2F2%29x-6 ALIGN=MIDDLE  ALT=\"+y+=-%283%2F2%29x-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> a slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%283%2F2%29 ALIGN=MIDDLE  ALT=\"-%283%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4x+-3y+-12=0 ALIGN=MIDDLE  ALT=\"+4x+-3y+-12=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > =><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=%284%2F3%29x-4 ALIGN=MIDDLE  ALT=\"+y+=%284%2F3%29x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> a slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2F3%29 ALIGN=MIDDLE  ALT=\"%284%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "these lines are not parallel, they have different slopes; it means, third given line must be parallel to one of these lines\r<BR>\n" );
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document.write( "find a slope of third line:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x+%2B4y+-11=0 ALIGN=MIDDLE  ALT=\"6x+%2B4y+-11=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%286%2F4%29x%2B11%2F4+ ALIGN=MIDDLE  ALT=\"y=-%286%2F4%29x%2B11%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%283%2F2%29x%2B11%2F4+ ALIGN=MIDDLE  ALT=\"y=-%283%2F2%29x%2B11%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" >=> a slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%283%2F2%29 ALIGN=MIDDLE  ALT=\"-%283%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, lines <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=-%283%2F2%29x-6 ALIGN=MIDDLE  ALT=\"+y+=-%283%2F2%29x-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-%283%2F2%29x%2B11%2F4+ ALIGN=MIDDLE  ALT=\"y=-%283%2F2%29x%2B11%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > are parallel\r<BR>\n" );
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document.write( "now, we need to find the distance between these parallel lines using distance formula: find one point on each line<BR>\n" );
document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=-6 ALIGN=MIDDLE  ALT=\"+y+=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > :(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-6 ALIGN=MIDDLE  ALT=\"-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=11%2F4+ ALIGN=MIDDLE  ALT=\"y=11%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" >:(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11%2F4=2.75 ALIGN=MIDDLE  ALT=\"11%2F4=2.75\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=sqrt%28%280-0%29%5E2%2B%282.75-%28-6%29%29%5E2%29 ALIGN=MIDDLE  ALT=\"d=sqrt%28%280-0%29%5E2%2B%282.75-%28-6%29%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=sqrt%28%282.75%2B6%29%5E2%29 ALIGN=MIDDLE  ALT=\"d=sqrt%28%282.75%2B6%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=8.75 ALIGN=MIDDLE  ALT=\"d=8.75\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "then we need to find a fourth line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=mx%2Bb ALIGN=MIDDLE  ALT=\"y=mx%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is parallel to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=%284%2F3%29x-4 ALIGN=MIDDLE  ALT=\"+y+=%284%2F3%29x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and will have a slope <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2F3%29 ALIGN=MIDDLE  ALT=\"%284%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=8.75 ALIGN=MIDDLE  ALT=\"d=8.75\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%284%2F3%29x%2Bb ALIGN=MIDDLE  ALT=\"y=%284%2F3%29x%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "find one point on <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=%284%2F3%29x-4 ALIGN=MIDDLE  ALT=\"+y+=%284%2F3%29x-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y+=-4 ALIGN=MIDDLE  ALT=\"+y+=-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >:(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4 ALIGN=MIDDLE  ALT=\"-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8.75=sqrt%28%28y-%28-4%29%29%5E2%29 ALIGN=MIDDLE  ALT=\"8.75=sqrt%28%28y-%28-4%29%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8.75=y%2B4 ALIGN=MIDDLE  ALT=\"8.75=y%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8.75-4=y ALIGN=MIDDLE  ALT=\"8.75-4=y\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4.75=y ALIGN=MIDDLE  ALT=\"4.75=y\"   DISABLED_style= \"max-width:90%; height:auto;\" >...point on a line we are looking for is :(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4.75 ALIGN=MIDDLE  ALT=\"4.75\"   DISABLED_style= \"max-width:90%; height:auto;\" >) which is y-intercept or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, our line is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=%284%2F3%29x%2B4.75%29 ALIGN=MIDDLE  ALT=\"highlight%28y=%284%2F3%29x%2B4.75%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\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-3x%2F2-6%2C+4x%2F3-4%2C-6x%2F4%2B2.75%2C%284%2F3%29x%2B4.75%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" );