Coordinates of a point on a line

[gene.finley]

I was reading the response to this question on the question bank
Question:
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?
Answer:
Point B is on line AC, two-thirds of the way between Point A and Point C. To find the coordinates of point B, it is helpful to imagine that you are a point traveling along line AC.

When you travel all the way from point A to point C, your x-coordinate changes 3 units (from x = 0 to x = 3). Two-thirds of the way there, at point B, your x-coordinate will have changed 2/3 of this amount, i.e. 2 units. The x-coordinate of B is therefore x = 0 + 2 = 2.
When you travel all the way from point A to point C, your y-coordinate changes 6 units (from y = -3 to y = 3). Two-thirds of the way there, at point B, your y-coordinate will have changed 2/3 of this amount, i.e. 4 units. The y-coordinate of B is therefore y = -3 + 4 = 1.

Thus, the coordinates of point B are (2,1).


I am having a very difficult time understanding the answer. I am unsure how we determined that point B was 2/3 the way between A and C. At first I thought this might related to the slope but that wasn't it. How did we come up with 2/3?

[tim]

That's from the AB = 2BC, which indicates in English that the distance from A to B is twice the distance from B to C. Draw a picture on your paper with that constraint and you'll see that B is 2/3 of the way from A to C.