Question 1127347
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The phrase "least value of line AC + line CB" has no meaning.  Lines don't have "values".<br>
And lines don't have lengths, either.  Mathematically, a line extends infinitely in both directions.<br>
What you are clearly looking for in this problem is the minimum total length of line SEGMENTS AC and CB.  Or more simply, the shortest total distance from A to C to B.<br>
The standard method of solution for this problem is to define point D to be the reflection in the x-axis of A: D(-1,-6).  Then the distance from A to C is the same as the distance from D to C.  And since the shortest distance between two point is a straight line, the shortest distance from A to C to B is the length of segment DB.<br>
Segment DB has horizontal and vertical components of 15 each; the Pythagorean Theorem gives the answer to the problem as 15*sqrt(2).