Start with a line segment connecting two points, A and B. 
means DA is 3 times longer than BA. Clearly, D cannot fall between A and B because that would mean DA is shorter than BA. So there are two possible locations where D can be placed on the line relative to A and B.
But with 
, or the fact that DB is 2 times longer than BA, we can rule out one of these positions; referring to the attachment, if we place D to the left of A, then DB would be 4 times longer than BA.
Finally, 
, so that CB is 2 times longer than AB. Again we have two possible locations for point C (it cannot fall between A and B), but one of them forces C to occupy the same point as D. However, A, B, C, D are distinct, so C must fall to the left of A.
Now let 
be the length of AB. Then the length of CD in terms of is 
. We have the coordinates of C and D, and the distance between them is 
. So
The slope of the line through C and D is
and so the equation of the line through these points is
So the coordinates of A are 
. The distance between C and A is 
, so we have
Since A falls to the right of C (in the 
plane, not just in the sketch), we know to take the positive value 
. Then the 
coordinate is 
.
All this to say that A is the point (1, 3), so
