document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=798046>Question 798046</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (a) The coordinates of the points P and Q are (6,4) and (-2,0) respectively. T is the point on PQ such that PT over TQ equals r. Write down the coordinates of T in terms of r.\r<BR>\n" );
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document.write( "(b) Given two lines L(1): x+7y-23=0 and L(2): 5x-4y+15=0. Find the equation of the line L(3) passing through the intersection of L(1) and L(2) and perpendicular to PQ.\r<BR>\n" );
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document.write( "(c) Using the result of (a) or otherwise, find the ratio in which L(3) divides PQ.\r<BR>\n" );
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document.write( "Please help me! I don't really understand! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #482039 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=482039\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Part (c) is not clear.  Part (a) does not ask for an exact numeric answer.  Part (b) seems clear enough.  \r<BR>\n" );
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document.write( "Part (b):<BR>\n" );
document.write( "Find the intersection, a point, of L1 and L2.  Find the slope of PQ and determine the slope of a perpendicular line to PQ.  Use the point-slope form for a line with this slope and point of intersection of L1 and L2 to find the equation for the line.  \r<BR>\n" );
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document.write( "L1:  x+7y=23<BR>\n" );
document.write( "L2:  5x-4y=-15\r<BR>\n" );
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document.write( "L1 is also <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2B35y=5%2A23 ALIGN=MIDDLE  ALT=\"5x%2B35y=5%2A23\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5x%2B35y=115 ALIGN=MIDDLE  ALT=\"5x%2B35y=115\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "L1-L2 is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285x%2B35y%29-%285x-4y%29=115-%28-15%29 ALIGN=MIDDLE  ALT=\"%285x%2B35y%29-%285x-4y%29=115-%28-15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=39y=130 ALIGN=MIDDLE  ALT=\"39y=130\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=13%2A10%2F%283%2A13%29 ALIGN=MIDDLE  ALT=\"y=13%2A10%2F%283%2A13%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=10%2F3 ALIGN=MIDDLE  ALT=\"y=10%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "From L1, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=23-7y ALIGN=MIDDLE  ALT=\"x=23-7y\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=23-7%2810%2F3%29 ALIGN=MIDDLE  ALT=\"x=23-7%2810%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=23%2A3%2F3-70%2F3 ALIGN=MIDDLE  ALT=\"x=23%2A3%2F3-70%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=69%2F3-70%2F3 ALIGN=MIDDLE  ALT=\"69%2F3-70%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1%2F3 ALIGN=MIDDLE  ALT=\"x=-1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Intersection of L1 and L2 is at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1%2F3 ALIGN=MIDDLE  ALT=\"x=-1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=10%2F3 ALIGN=MIDDLE  ALT=\"y=10%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Slope of PQ:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284-0%29%2F%286-%28-2%29%29=1%2F2 ALIGN=MIDDLE  ALT=\"%284-0%29%2F%286-%28-2%29%29=1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "A line perpendicular to PQ must have a slope of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The line perpendicular to PQ and containing the point (-1/3, 10/3) is, using the point-slope form, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-10%2F3=-2%28x-%28-1%2F3%29%29 ALIGN=MIDDLE  ALT=\"y-10%2F3=-2%28x-%28-1%2F3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-10%2F3=-2x-2%2F3 ALIGN=MIDDLE  ALT=\"y-10%2F3=-2x-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=3y-10=-6x-2 ALIGN=MIDDLE  ALT=\"3y-10=-6x-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%2B3y=10-2 ALIGN=MIDDLE  ALT=\"6x%2B3y=10-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%2B3y=8 ALIGN=MIDDLE  ALT=\"6x%2B3y=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Standard Form; or if you prefer, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%2B3y-8=0 ALIGN=MIDDLE  ALT=\"6x%2B3y-8=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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