document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1131594>Question 1131594</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the equation that is satisfied by the coordinates of each point. A rod PQ of the length 12 moves so that P is always on the Y-axis and Q always on the X-axis. A point M on PQ is 2/3 of the way from P to Q. What equation is satisfied by the coordinates of M? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #748803 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=748803\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
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document.write( "From the length of the rod, you know,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-0%29%5E2%2B%280-y%29%5E2=12%5E2 ALIGN=MIDDLE  ALT=\"%28x-0%29%5E2%2B%280-y%29%5E2=12%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2=144 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2=144\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and then you know that for the x coordinate,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a-0%29%2F%28x-0%29=2%2F3 ALIGN=MIDDLE  ALT=\"%28a-0%29%2F%28x-0%29=2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Fx=2%2F3 ALIGN=MIDDLE  ALT=\"a%2Fx=2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3a=2x ALIGN=MIDDLE  ALT=\"3a=2x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%283%2F2%29a ALIGN=MIDDLE  ALT=\"x=%283%2F2%29a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and for the y coordinate,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28b-y%29%2F%280-y%29=2%2F3 ALIGN=MIDDLE  ALT=\"%28b-y%29%2F%280-y%29=2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28b-y%29=-2y ALIGN=MIDDLE  ALT=\"3%28b-y%29=-2y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3b-3y=-2y ALIGN=MIDDLE  ALT=\"3b-3y=-2y\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3b ALIGN=MIDDLE  ALT=\"y=3b\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So plugging back into the length equation,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%283%2F2%29a%29%5E2%2B%283b%29%5E2=144 ALIGN=MIDDLE  ALT=\"%28%283%2F2%29a%29%5E2%2B%283b%29%5E2=144\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289%2F4%29a%5E2%2B9b%5E2=144 ALIGN=MIDDLE  ALT=\"%289%2F4%29a%5E2%2B9b%5E2=144\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%289a%5E2%2B36b%5E2=576%29 ALIGN=MIDDLE  ALT=\"highlight%289a%5E2%2B36b%5E2=576%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Just to verify, <BR>\n" );
document.write( "when <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;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=0 ALIGN=MIDDLE  ALT=\"a=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the point Q is at the origin, PQ lies entirely on the y axis,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9a%5E2%2B36b%5E2=576 ALIGN=MIDDLE  ALT=\"9a%5E2%2B36b%5E2=576\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36b%5E2=576 ALIGN=MIDDLE  ALT=\"36b%5E2=576\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2=4 ALIGN=MIDDLE  ALT=\"b%5E2=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Two solutions : <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=2 ALIGN=MIDDLE  ALT=\"b=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-2 ALIGN=MIDDLE  ALT=\"b=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Two thirds from P to Q would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F3%29%2812%29=8 ALIGN=MIDDLE  ALT=\"%282%2F3%29%2812%29=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > since P is at (0,12) then M should be at (0,12-8)=(0,4), which is consistent to the answer from the equation. P could also be at (0,-12). Similary 2/3 from P to Q would be (0,-12+8)=(0,-4).<BR>\n" );
document.write( "You can do the same check when PQ is entirely on the x-axis just to verify (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=0 ALIGN=MIDDLE  ALT=\"b=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
document.write( " </SPAN>\n" );
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