Hypothetical (1 Viewer)

[skypryn]

um this may have been asked before and perhaps it's a stupid question but for the formula to find a point dividing two lines either internally or externally, couldn,t there be two answers? like when you think about it you could divide a line in a given ratio in two seperate ways...eg

----.--

--.----

same ratio - 2:1 internal

two seperate answers?

 

[CM_Tutor]

There will usually only be one answer, becuase the question will usually dictate how to divide the interval. ie. "Find the point P that divides the interval AB in the ratio x:y means that PA / PB = x / y" - that is, the interval AB is directed, it starts at A.

However, a question could be asked in which there are more than one answer. For example: If A and B are (give coordinates), and they lie on a line l, find all points P on l where the distance from P to one of the points is twice the distance from P to the other. This question would have four answers for P, two between A and B on l - as in your diagram. The question could focus on these two by saying 'find all point P between A and B on l'.

Note: I can't recall such a question being asked, but it is possible.

 

[skypryn]

yeah alright - so the order in which the points are listed dictates the interval? thanks

 

[DcM]

Originally posted by CM_Tutor
This question would have four answers for P, two between A and B on l - as in your diagram.

wheres the other two answers?

 

[CM_Tutor]

Originally posted by DcM
wheres the other two answers?

The two cases where P externally divides the interval.

 

[DcM]

ohhh...
but i thort the point P has to be on the interval..

wait...the line l continues on rite?? ohh i get it..

 

[CM_Tutor]

Originally posted by DcM
wait...the line l continues on rite?? ohh i get it..

Yes, a line continues in two directions (ie <------->)
a ray continues in one direction (ie <-------* or *------->)
and an interval has fixed end points (ie *-------*)