A dog is being trained for tracking duties with a Search and Rescue group. The trainer sets up a course with the following coordinates as check points along the way, to see if the dog can follow a scent trail accurately.

$A=1\mathrm{.}80kmat21\mathrm{.}0$ West $of$ North

$B=4\mathrm{.}50kmat32\mathrm{.}0$ South $of$ West

$C=2\mathrm{.}05km$ due North

$D=1\mathrm{.}75kmat62\mathrm{.}0$ North $of$ East

What is the overall displacement of the dog and trainer from start to finish?

$**$ Explain the steps used in your solution in a short paragraph.

$\frac{1}{10}$

$15$