document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=988589>Question 988589</A>: <I><SPAN STYLE=\"word-break: break-all;\"> HI, this question is from my textbook.<BR>\n" );
document.write( "The equations of two sides of a square are y=3x-1 and x+3y-6=0. (0,-1) is one vertex of the square. Find the coordinates of the other vertices. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #609141 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=609141\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3x-1 ALIGN=MIDDLE  ALT=\"y=3x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3y-6=0 ALIGN=MIDDLE  ALT=\"x%2B3y-6=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > are the equations of two sides of the square.<BR>\n" );
document.write( "The coordinates of the vertex at the intersection of those two sides can be found by solving the system<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28y=3x-1%2Cx%2B3y-6=0%29 ALIGN=MIDDLE  ALT=\"system%28y=3x-1%2Cx%2B3y-6=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28y=3x-1%2Cx%2B3%283x-1%29-6=0%29 ALIGN=MIDDLE  ALT=\"system%28y=3x-1%2Cx%2B3%283x-1%29-6=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28y=3x-1%2Cx%2B9x-3-6=0%29 ALIGN=MIDDLE  ALT=\"system%28y=3x-1%2Cx%2B9x-3-6=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28y=3x-1%2C10x-9=0%29 ALIGN=MIDDLE  ALT=\"system%28y=3x-1%2C10x-9=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28y=3x-1%2Cx=9%2F10%29 ALIGN=MIDDLE  ALT=\"system%28y=3x-1%2Cx=9%2F10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28y=3%289%2F10%29-1%2Cx=9%2F10%29 ALIGN=MIDDLE  ALT=\"system%28y=3%289%2F10%29-1%2Cx=9%2F10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28y=27%2F10%29-10%2F10%2Cx=9%2F10%29 ALIGN=MIDDLE  ALT=\"system%28y=27%2F10%29-10%2F10%2Cx=9%2F10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28system%28y=17%2F10%2Cx=9%2F10%29%29 ALIGN=MIDDLE  ALT=\"highlight%28system%28y=17%2F10%2Cx=9%2F10%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "So, point (9/10,17/10), or (0.9,1.7) is one vertex,<BR>\n" );
document.write( "the one at the intersection of the two given sides.<BR>\n" );
document.write( "Point (0,-1) , with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x=0%2Cy=-1%29 ALIGN=MIDDLE  ALT=\"system%28x=0%2Cy=-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the other end/vertex of that side with equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3x-1 ALIGN=MIDDLE  ALT=\"y=3x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "So far we have this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-1%2C4%2C-2%2C3%2C%0D%0Agrid%280%29%2Carrow%28-2%2C-7%2C2%2C5%29%2C%0D%0Aarrow%28-6%2C4%2C6%2C0%29%2Cred%28line%280%2C-1%2C0.9%2C1.7%29%29%2C%0D%0Ared%28circle%280%2C-1%2C0.05%29%29%2Cred%28circle%280.9%2C1.7%2C0.05%29%29%2C%0D%0Alocate%280.1%2C-1.1%2Cred%28A%29%29%2Clocate%281%2C1.9%2Cred%28B%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "What we do not know is to what side of segment <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28AB%29 ALIGN=MIDDLE  ALT=\"red%28AB%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to draw the square.<BR>\n" );
document.write( "There are really two right answers. Which one will be the right one according to your textbook? Or did the authors realize that there were two possible answers?<BR>\n" );
document.write( "We can draw the square to the right, like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-1%2C4%2C-2%2C3%2C%0D%0Agrid%280%29%2C%0D%0Ared%28line%280%2C-1%2C0.9%2C1.7%29%29%2Cred%28line%283.6%2C0.8%2C2.7%2C-1.9%29%29%2C%0D%0Ared%28line%280%2C-1%2C2.7%2C-1.9%29%29%2Cred%28line%283.6%2C0.8%2C0.9%2C1.7%29%29%2C%0D%0Ared%28circle%280%2C-1%2C0.05%29%29%2Cred%28circle%280.9%2C1.7%2C0.05%29%29%2C%0D%0Ared%28circle%283.6%2C0.8%2C0.05%29%29%2Cred%28circle%282.7%2C-1.9%2C0.05%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > , or we can draw the square to the left, as Alan suggested.<BR>\n" );
document.write( "Either way, if we encase that square inside a larger square with sides parallel to the x- and y-axes,<BR>\n" );
document.write( "we form four congruent right triangles with legs measuring<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5BB%5D-x%5BA%5D=0.9-0=0.9 ALIGN=MIDDLE  ALT=\"x%5BB%5D-x%5BA%5D=0.9-0=0.9\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5BB%5D-y%5BA%5D=1.7-%28-1%29=2.7 ALIGN=MIDDLE  ALT=\"y%5BB%5D-y%5BA%5D=1.7-%28-1%29=2.7\"   DISABLED_style= \"max-width:90%; height:auto;\" > , like this <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-1%2C4%2C-3%2C2%2C%0D%0Agrid%280%29%2C%0D%0Ared%28line%280%2C-1%2C0.9%2C1.7%29%29%2Cred%28line%283.6%2C0.8%2C2.7%2C-1.9%29%29%2C%0D%0Ared%28line%280%2C-1%2C2.7%2C-1.9%29%29%2Cred%28line%283.6%2C0.8%2C0.9%2C1.7%29%29%2C%0D%0Ared%28circle%280%2C-1%2C0.05%29%29%2Cred%28circle%280.9%2C1.7%2C0.05%29%29%2C%0D%0Ared%28circle%283.6%2C0.8%2C0.05%29%29%2Cred%28circle%282.7%2C-1.9%2C0.05%29%29%2C%0D%0Aline%280%2C-1.9%2C0%2C1.7%29%2Cline%283.6%2C1.7%2C0%2C1.7%29%2C%0D%0Aline%283.6%2C-1.9%2C3.6%2C1.7%29%2Cline%283.6%2C-1.9%2C0%2C-1.9%29%2C%0D%0Alocate%280.05%2C-1.3%2C0.9%29%2Clocate%283.17%2C1.3%2C0.9%29%2C%0D%0Alocate%282.5%2C1.7%2C2.7%29%2Clocate%281.2%2C-1.65%2C2.7%29%2C%0D%0Arectangle%280%2C-1.9%2C0.2%2C-1.7%29%2Crectangle%283.6%2C1.7%2C3.4%2C1.5%29%2C%0D%0Arectangle%280%2C1.7%2C0.2%2C1.5%29%2Crectangle%283.6%2C-1.9%2C3.4%2C-1.7%29%2C%0D%0Alocate%280.05%2C-1%2Cred%28A%29%29%2Clocate%281%2C1.95%2Cred%28B%29%29%2C%0D%0Alocate%282.65%2C-1.96%2Cred%28F%29%29%2Clocate%283.67%2C0.9%2Cred%28E%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5BE%5D=x%5BB%5D%2B2.7=0.9%2B2.7=3.6 ALIGN=MIDDLE  ALT=\"x%5BE%5D=x%5BB%5D%2B2.7=0.9%2B2.7=3.6\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5BE%5D=y%5BB%5D-0.9=1.7-0.9=0.8 ALIGN=MIDDLE  ALT=\"y%5BE%5D=y%5BB%5D-0.9=1.7-0.9=0.8\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5BF%5D=x%5BA%5D%2B2.7=0%2B2.7=2.7 ALIGN=MIDDLE  ALT=\"x%5BF%5D=x%5BA%5D%2B2.7=0%2B2.7=2.7\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5BF%5D=y%5BA%5D-0.9=-1-0.9=-1.9 ALIGN=MIDDLE  ALT=\"y%5BF%5D=y%5BA%5D-0.9=-1-0.9=-1.9\"   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );