A conceptual question on "division of intervals" (1 Viewer)

[Sirius Black]

(1991 HSC Q1 c) ) The point P (-3,8) divides the interval AB externally in the ratio of k:1.
If A is the point (6,-4) and B is the point (0,4), find the value of k. (k=3 or -3 ?)

For this type of question, we were taught at school like "If the interval was divided externally, then the ratio is negative." However, the answer at the back of " Success One HSC" is positive i.e. k=3
But the answer on the book named "past HSC paper"-ish (which is published by NSW Mathematical Association) says the k= -3.
In this case, which one should we take if the question clearly states that "...externally in the ration of m:n..." ?

 

[prsce24]

they are both correct
if its externally ratio
you can either make -k:1
or k:-1

which gives the same answer

 

[prsce24]

i got k=3

agagsdfdsafsgadg

 

[mojako]

strictly speaking, if the sentence says:
"divides externally in the ratio k : 1",
k is positive.
If the sentence says:
"divides in the ratio k : 1" and it also says externally in another clause of the sentence (or in another sentence),
k is negative.

when you put k into the standard formula (the same formula you use when it was internal division),
you put k as negative.

in the answer to that particular question, I would write
"P divides AB externally in the ratio 3 : 1, i.e. P divides AB in the ratio -3 : 1"
and avoid writing k = something.