Re: Is |a b| < |a c| ? (1) a > 0 (2) |b| < |c|
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21 Mar 2023, 22:13
Is |a − b| < |a − c| ?
Interpretation - is b farther away from a than what c is from a. In other words, is the distance between b and a greater than the distance between c and a
(1) a > 0
Interpretation - a is to the right of centre (0,0)
- still gives us no possible idea about location of b and c
- b can be farther away from a than c, or the opposite also can be possible.
(2) |b| < |c|
interpretation - c is farther away from the centre (0,0) than b
- gives us no possible idea about the location of a
- a can be closer to c than b, or the opposite is also possible
combine (1) and (2)
- a is to the right of centre (0,0) and c is farther away from centre than b is
three possible scenarios:
Case 1
-----[0]------------[a]---------------[b]-----------------[c]
Case 2
---------[0]-----------------------[b]----------------[c]-------------------[a]-------------------------
Case 3
--------[0]---------------[b]-----------[a]-----------------[c]---------------------------------------------
As you can see, many cases are possible,
Case 4
--------------[c]-----------------------[0]-------------------[a]------------------[b]-------------------------
Case 5
---------------[c]-------------[0]-----------------[b]---------------------[a]-------------------------
Case 6
---------------[c]-----------[b]------------[0]----------[a]-------------------------
Therefore both statements together are also not sufficient