Explanation:

- Let's break down the positions of each friend based on the information given.

- B is the start point. C is 3 km north of B.

- D is 3 km south of B (thus, directly aligned with B vertically).

- A is 2 km west of B.

- E is 4 km west of D (horizontally aligned with D).

- F is 5 km south of E.

Now, calculate the shortest distance between F and C:

- C is 3 km north of B. D is 3 km south of B. So, C is 6 km north of D.

- E, being 4 km west of D, means F is also 5 km directly south of E (6 km north of D puts C above D by 6 km and F moves west by 4 km).

- Using coordinates:

- C's position relative to B is (0, 3).

- F’s position relative to B is (4, -8) since it’s west and south.

- Calculate the distance: $\sqrt{(0-4{)}^2+(3-(-8){)}^2}=\sqrt{16+121}=\sqrt{137}$ km.

- Option 4: v137 km is indeed the correct answer.

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