Let (x,y) and (v,w) two points, if (p,q) divides the segment with end points (x,y) and (v,w) at a ratio a:b we can set the following equalities:

Substituting the given data we get that:

Simplifying the above result we get:

Therefore the coordinates of point P such that the segment with endpoints A (2, 4) and B (17, 14) in a ratio of 2:3 are (8,8).
Answer:
