First a quick rant on my part. If you're going to get proficient in mathematics, you must learn to say what you mean, and mean what you say. What you meant to say is:not:which is what you (and sa-ri-ga-ma) wrote.
Even if you don't know how to use LaTeX (and there's lots of information on this web-site) there's no excuse for leaving out brackets. What you mean is:
x3 = (rx1 + sx2)/(r + s), y3 = (ry1 + sy2)/(r + s)Next, which way round do the and go? The answer is that they 'flip' over.
So that if the point divides the line joining to in the ratio , then the and 'flip' over in the formula, with the going with the and the with .
Therefore, in the formula above:where goes with and and with and , the point divides the line joining to in the ratio - not .
It's easy to see why if you think of being large compared to .
For instance if , and divides in the ratio , then is much closer to than it is to . So its coordinates will be much nearer 's than 's. So we shall need more and less . Therefore the bigger number ( ) will go with and the smaller ( ) with . They 'flip' over.
Do you get it now?