When dividing a line into an a certain internal ratio using two points A and B, it seems like it does matter which point you assign as (x1, y1) and which is (x2, y2). Could someone please explain why, with an example to help clarify?

Question

ganeshie8 · Answer

yes, it matters. whats confusing you ?

ganeshie8 · Answer

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ganeshie8 · Answer

dividing AB into 1:10 ratio is not same as dividing BA into 1:10 ratio

anonymous · Answer

I don't understand why it matters. If I was to find the gradient between two points, it wouldn't make a difference which x-value I assign as x1 or x2.

anonymous · Answer

So what you're saying is that the first point is implied as the point on the left, with the "left" number in the ratio implied to be the part of the ratio closest to the left point?

ganeshie8 · Answer

Exactly !!! for gradient it wouldnt matter, but when u divide a segment, it matters

anonymous · Answer

Ok - I understand, but it doesn't seem 100% mathematically sound to me. Thanks for your help.

ganeshie8 · Answer

lol what do you mean doesnt seem mathematically, you want a proof or what :)

anonymous · Answer

Generally it makes sense but the question I had involved two points that weren't given specific point labels and I was then just told to find the point that divides them in a ratio, without it saying something like "divide AB into the ratio X:Y". In those situations, it seems like I could pick either point as having (x1, y1) co-ordinates assigned to it, which I can't, so I had to assume that the point with the lesser x-value was (x1, y1) for the ratio formula to work.
I hope that makes sense lol