Question 1144732
AB+BC is smallest when A, B, and C are collinear (lie on the same straight line).<br>
Use any of a number of methods to find the value of k that makes the three points collinear.<br>
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>
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.