If Point x is on segment PQ so that the length of segment PX is twice the length of segment XQ what are the coordinates of point x?

For the conditions stated, if one line segment (PX) is twice the length of the other (XQ), then point X must be 2/3 of the way towards Q because let s = the length of XQ and 2s = length of PX

2s / (2s +s) = 2s / 3s = 2/3

Therefore, if we go 2/3 the distance in the x direction from point P and 2/3 the distance in the y direction from point P, we will arrive at the location for point X.

So this turns out to be

(2/3) × (18-6) = 8 in the X direction

AND

(2/3) × (8-2) = 4 in the Y direction

And our final answer is :

(X,Y) = (6+8, 2+4) = (14, 6)