Vectors and finding points on a line

Question

Long John Silver, a pirate, has buried his treasure on an island with five trees located at the following points: A (30.0m, -20.0m), B(60.0 m, 80.0m), C (-10.0m, -10.0m), D (40.0m, -30.0m), and E(-70.0m, 60.0m). All of the points are measured relative to some origin. Long John's map instructs you to start at A and move toward B, but cover only one-half the distance between A and B. Then move toward C, covering one-third the distance between your current location and C. Then move toward D, covering one-fourth the distance between where you are and D. Finally, move toward E, covering one-fifth the distance between you and E, stop and dig. (a) What are the coordinates of the point where the pirate's treasure is buried?...after trying several formulas that I know and looking at the internet for help, I haven't been able to find an answer. If anyone can please help me it will be much appreciated.

Answer 1

Hint: The $x$ coordinate of the point a fraction $p$ from $S$ to $T$ is $x_S +p(x_T-x_S)$, and similarly with the $y$ coordinate. Just work through the calculations

Here is a diagram to help (I think)

Answer 2

The locations are:

P1 = A + (B - A) / 2
P2 = P1 + (C - P1) / 3
P3 = P2 + (D - P2) / 4
P4 = P3 + (E - P3) / 5    == treasure location

Each equation are in fact 2 equations for the x and y coordinates respectively.

B - A is the vector from A to B. When you are in A and move along the vector B - A you arrive at A + (B - A) = B. When you move only half of the distance you arrive at P1 = A + (B - A)/2.