document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=175453>Question 175453</A>: <I><SPAN STYLE=\"word-break: break-all;\"> point C lies on line AB such that AC= 3/4 AB.  If the endpoints of line AB are  A(8,12) and B(-4,0) ,find C.\r<BR>\n" );
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document.write( "       i know i have to use substitution but its been a couple months since I have had a problem like this. If you could please guide me through the steps you would be very helpful.  Thank You </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #130575 by </B><A HREF=/tutors/aboutme.mpl?userid=psbhowmick><B>psbhowmick(878)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=psbhowmick><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=psbhowmick><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=130575\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If straight line AB is divided by the point such that AC:CB = m:n then the projections of AB on x and y axes will also be divided in the same ratio.\r<BR>\n" );
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document.write( "Let the coordinates of the points be denoted by the name of the point with a suffix x or y. Thus coordinates of C are (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5Bx%5D ALIGN=MIDDLE  ALT=\"C%5Bx%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5By%5D ALIGN=MIDDLE  ALT=\"C%5By%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and so on.\r<BR>\n" );
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document.write( "Considering the projection on x axis,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28A%5Bx%5D+-+C%5Bx%5D%29%2F%28C%5Bx%5D+-+B%5Bx%5D%29+=+m%2Fn ALIGN=MIDDLE  ALT=\"%28A%5Bx%5D+-+C%5Bx%5D%29%2F%28C%5Bx%5D+-+B%5Bx%5D%29+=+m%2Fn\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%28A%5Bx%5D+-+C%5Bx%5D%29+=+m%28C%5Bx%5D+-+B%5Bx%5D%29 ALIGN=MIDDLE  ALT=\"n%28A%5Bx%5D+-+C%5Bx%5D%29+=+m%28C%5Bx%5D+-+B%5Bx%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5Bx%5D+=+%28n%2AA%5Bx%5D+%2B+m%2AB%5Bx%5D%29%2F%28m%2Bn%29 ALIGN=MIDDLE  ALT=\"C%5Bx%5D+=+%28n%2AA%5Bx%5D+%2B+m%2AB%5Bx%5D%29%2F%28m%2Bn%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ___________ (1)\r<BR>\n" );
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document.write( "In a similar way, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5By%5D+=+%28n%2AA%5By%5D+%2B+m%2AB%5By%5D%29%2F%28m%2Bn%29 ALIGN=MIDDLE  ALT=\"C%5By%5D+=+%28n%2AA%5By%5D+%2B+m%2AB%5By%5D%29%2F%28m%2Bn%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ____________ (2)\r<BR>\n" );
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document.write( "If the point lies outside the line segment AB then m/n will be negative as AC and CB will be in opposite directions.\r<BR>\n" );
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document.write( "Here, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bx%5D+=+8 ALIGN=MIDDLE  ALT=\"A%5Bx%5D+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5By%5D+=+12 ALIGN=MIDDLE  ALT=\"A%5By%5D+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B%5Bx%5D+=+-4 ALIGN=MIDDLE  ALT=\"B%5Bx%5D+=+-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B%5By%5D+=+0 ALIGN=MIDDLE  ALT=\"B%5By%5D+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and m/n =  +- 3 (- sign comes because C may be outside the line segment AB as well). Let m = +-3k and n = k (k = arbitrary constant).\r<BR>\n" );
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document.write( "Substituting these in (1) we have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5Bx%5D+=+%28k%2A8+%2B-+3k%2A%28-4%29%29%2F%28%2B-3k+%2B+k%29 ALIGN=MIDDLE  ALT=\"C%5Bx%5D+=+%28k%2A8+%2B-+3k%2A%28-4%29%29%2F%28%2B-3k+%2B+k%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Either <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5Bx%5D+=+%288k+-+12k%29%29%2F%283k+%2B+k%29 ALIGN=MIDDLE  ALT=\"C%5Bx%5D+=+%288k+-+12k%29%29%2F%283k+%2B+k%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5Bx%5D+=+%288k+%2B+12k%29%29%2F%28-3k+%2B+k%29 ALIGN=MIDDLE  ALT=\"C%5Bx%5D+=+%288k+%2B+12k%29%29%2F%28-3k+%2B+k%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Either <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5Bx%5D+=+-1 ALIGN=MIDDLE  ALT=\"C%5Bx%5D+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5Bx%5D+=+-10 ALIGN=MIDDLE  ALT=\"C%5Bx%5D+=+-10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Substituting into (2) we have<BR>\n" );
document.write( "Either <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5By%5D+=+3 ALIGN=MIDDLE  ALT=\"C%5By%5D+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5By%5D+=+-6 ALIGN=MIDDLE  ALT=\"C%5By%5D+=+-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the possible set of coordinates of C are (-1, 3) and (-10, -6).\r<BR>\n" );
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