13.9 The minimum value of $|x-1|+|x-2|+|x-3|$ is
(A) 1 .
(B) 2 .
(C) 3 .
(D) 4 .
(Anhui Province, China Junior High School Mathematics Competition, 1996)
[Solution] As shown in the figure, given
$|x-1|+|x-2|+|x-3|$
can be replaced by $P A+P B+P C$.
It is easy to know: when $P$ coincides with $B$, $P A+P B+P C$ is minimized.
That is, the minimum value of $|x-1|+|x-2|+|x-3|$ is 2.
Therefore, the answer is $(B)$.