# what does it mean that plane XY divides the line joining (2,4,5) & (3,5,-4) with a negative ratio

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?

• Your question is not clear: please explain in more detail. – Aretino Apr 14 at 11:40
• 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. – David K Apr 14 at 11:45
• We all see a lot of nonsense when we're in high school. I wouldn't worry about it. – Gerry Myerson Apr 14 at 13:10
• I edited, changed the entire question to a one the makes sense but still will give me my answer – Ahmed I. Elsayed Apr 14 at 16:41
• @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. – user376343 Apr 14 at 19:20