What does it mean that plane $XY$ divides the line joining $(2,4,5) \text{ and } (3,5,-4)$ with a negative ratio?

It's an old question I saw when I was in high school. Search results didn't help.

I understand how it is divided and how to get the ratio so I don't need to provide how I got it, I just don't understand why the ratio is negative, As I remember it was $-2:3$ and I got $2:3$ in many tries.

I don't want someone to fix my answer to get the negative ratio, I want someone to explain what does it mean to get a negative ratio?

  • $\begingroup$ Your question is not clear: please explain in more detail. $\endgroup$ – Aretino Apr 14 at 11:40
  • $\begingroup$ If you can recall an example of a problem where you saw this notation, it would help. With no other information, I would guess there are already two points $A$ and $B$ on the second line, the ratio represents something about the position of the intersection point $C$ relative to these, and the sign of the ratio has something to do with which of the points is between the other two. $\endgroup$ – David K Apr 14 at 11:45
  • $\begingroup$ We all see a lot of nonsense when we're in high school. I wouldn't worry about it. $\endgroup$ – Gerry Myerson Apr 14 at 13:10
  • $\begingroup$ I edited, changed the entire question to a one the makes sense but still will give me my answer $\endgroup$ – Ahmed I. Elsayed Apr 14 at 16:41
  • 1
    $\begingroup$ @Ahmed I. Elsayed An explanation that comes to my mind is: if the given points are $A,B$ and the intersection is $P,$ then the vectors verify $2PA=-3PB.$ In other words, the sign can be related to an ancient notation, where a ratio is not only ratio of lengths, but also mutual orientation of segments. $\endgroup$ – user376343 Apr 14 at 19:20

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