document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1144732>Question 1144732</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The coordinates of points A, B, and C are A(-4,9), B(k,0), and C(8,3). What is the value of k, which causes the sum AB+BC to be as small as possible? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #765908 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</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=765908\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> AB+BC is smallest when A, B, and C are collinear (lie on the same straight line).<br><BR>\n" );
document.write( "Use any of a number of methods to find the value of k that makes the three points collinear.<br><BR>\n" );
document.write( "I prefer logical reasoning, using an UNDERSTANDING of the slope of a line, along with simple arithmetic, over formal algebra where it is practical, as it is in this problem.<br><BR>\n" );
document.write( "From A to C is 12 to the right and 6 down, for a ratio of 2 to the right and 1 down.  (A slope of -1/2, if you prefer.)  To get y from 3 at point C to 0, I need to go down 3, which means I need to go right 6; so the value of k is 8+6 = 14. </SPAN>\n" );
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