Coordinates Question

[rjcesaro]

The coordinates of points A and C are (0, -3) and (3, 3), respectively. If point B lies on line AC between points A and C, and if AB = 2BC, which of the following represents the coordinates of point B?

This comes from the geometry math bin questions. I don't understand the explanation as it relates to the 2/3 portion. Thanks.

[debmalya.dutta]

its given AB = 2BC
AB + BC = AC
AB + AB/2 = AC
3/2 AB = AC
So , point B which lies on the line joining A and C divides the line in such a way that the following ratio holds good

AB/AC = 2/3


The coordinates of a point on a line when the line is divided in the ratio m:n.and given that the end points of the line are with coordinates (x1,y1)and(x2,y2), then the coordinates of this point would be;
x = (nx1 + mx2)/(m+n)
y = (ny1 + my2)/(m+n)

[tim]

Thanks debmalya. Yeah you can set up some algebraic equations to verify the fraction, or you can just think of it this way: if one part of something is twice the other part, it is 2/3 of the whole thing (and the smaller part is 1/3)..