document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=158662>Question 158662</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780495554035/algebrahomeworkh>College Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> The Question is:<BR>\n" );
document.write( "Consider the line segment determined by A(-1,2) and B(5,11). Find the coordinates of a point P such that AP/PB=2/1.\r<BR>\n" );
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document.write( "I have no idea where to start with this problem... My solution manual states that the point \"must\" lie 2/3 of the distance from A to B.<BR>\n" );
document.write( "My question is... How does someone find out that the point \"must\" be 2/3 the distance from A to B.<BR>\n" );
document.write( "I understand from the problem that line segment AP is twice as long as line segment PB. I found a midpoint (2,13/2) and the quarter point (7/2,35/4)and thought somehow I could come up with the 2/3 that they start with in the manual.<BR>\n" );
document.write( "Please explain how you get to the 2/3 distance.<BR>\n" );
document.write( "Thanks to all you tutors out there! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #116974 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=116974\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Consider the line segment determined by A(-1,2) and B(5,11). Find the coordinates of a point P such that AP/PB=2/1.<BR>\n" );
document.write( "I have no idea where to start with this problem... My solution manual states that the point \"must\" lie 2/3 of the distance from A to B.<BR>\n" );
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document.write( "Think of the segment as being the hypotenuse of a right triangle.<BR>\n" );
document.write( "Plotting this segment on graph paper will illustrate this.<BR>\n" );
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document.write( "Note that:<BR>\n" );
document.write( "the horizontal side is 5 -(-1) = 6 units<BR>\n" );
document.write( "the vertical side is 11 - 2 = 9 units<BR>\n" );
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document.write( "Find the 2/3 segment:<BR>\n" );
document.write( "Horizontal side  = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >* 6 = 4 units<BR>\n" );
document.write( "Vertical side = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >* 9 = 6 units<BR>\n" );
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document.write( "Find the xy coordinates of 2/3 the segment:<BR>\n" );
document.write( "x:  4 - 1 = 3<BR>\n" );
document.write( "y:  6 + 2 = 8<BR>\n" );
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document.write( "xy Coordinates of 2/3 segment: 3, 8<BR>\n" );
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document.write( "You can prove this, find the hypotenuse of the original line<BR>\n" );
document.write( "h = Sqrt(6^2 + 9^2) = 10.8167<BR>\n" );
document.write( "The hypotenuse of the 2/3 segment<BR>\n" );
document.write( "h = Sqrt(4^2 + 6^2) = 7.2111<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7.2111%2F10.8167 ALIGN=MIDDLE  ALT=\"7.2111%2F10.8167\"   DISABLED_style= \"max-width:90%; height:auto;\" > = .6666 ~ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Did this help?\r<BR>\n" );
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document.write( " </SPAN>\n" );
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