document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1106556>Question 1106556</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the coordinates of point P that divides the segments with the given endpoints in the ratio 2 : 3.<BR>\n" );
document.write( "i A(-3, -1) and B(2, 4) iii A(-2, -3) and B(4, 0)<BR>\n" );
document.write( "ii A(-4, 9) and B(1, -1) iv A(-6, -1) and B(3, 8) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #721591 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13209)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=721591\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The solution by the first tutor is wrong.<br><BR>\n" );
document.write( "Adding 2/3 of the distance between the two endpoints to each of the x and y coordinates of the first endpoint does not give you the coordinates of point P.<br><BR>\n" );
document.write( "Furthermore, if P divides segment AB into two parts in the ratio 2:3, then point P is 2/5 of the distance from A to B -- not 2/3 of the distance.<br><BR>\n" );
document.write( "To find the coordinates of point P in each case, it is much easier to work with the x and y components separately, rather than working with the distance between the endpoints.<br><BR>\n" );
document.write( "i) A(-3,-1) and B(2,4)<BR>\n" );
document.write( "The difference in the x coordinates is 5; the difference in the y coordinates is also 5.  2/5 of 5 is 2; so point P is 2 units in the x direction and 2 units in the y direction from A, giving you P(-1,1).<br><BR>\n" );
document.write( "ii) A(-2,-3) and B(4,0)<BR>\n" );
document.write( "The difference in the x coordinates is 6; the difference in the y coordinates is 3.  2/5 of 6 is 2.4; 2/5 of 3 is 1.2; so point P is 2.4 units in the x direction and 1.2 units in the y direction from A, giving you P(0.4,-1.8).<br><BR>\n" );
document.write( "The other two cases are worked in the same way....<BR>\n" );
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