Hello kullgirl418Continuing from my reply to your previous post, we can generalise the result about the position vector of the mid-point of a line segment, to get the position vector of a point dividing a line segment in a given ratio, and it's this:

The position vector of the point that divides the line segment in the ratio is given by:So suppose the triangle is is the mid-point of and divides in the ratio . Then:

, as before using the mid-point formulaand:

, using the more general result aboveNow you'll see that is the point that's two-thirds of the way down the median . I'll leave it to you to show that it's also two-thirds of the way down the other medians as well. (Although this is pretty obvious since the expression for is symmetrical in and .)

Grandad