Analyze the provided details thoroughly and answer the subsequent question.

An automated delivery drone departs from distribution center F and flies due west. After traveling 27m, it hovers at waypoint D. It then makes a left turn, flies for another 20m, and reaches waypoint C. From waypoint C, the drone turns right and travels for 27m to waypoint B. Finally, it makes a right turn and travels 10m to land at destination A.

What is the direction of the drone's destination A with respect to its initial departure point F?

The correct option is South-west.

To find the direction of destination A with respect to the initial departure point F, let us trace the path of the drone step-by-step by placing starting point F at the origin (0, 0) on a standard directional grid (where East is +x, West is -x, North is +y, and South is -y):

1. Movement from F to Waypoint D:
The drone flies due West from F for 27 m.
Coordinates of D = (-27, 0)

2. Movement from Waypoint D to Waypoint C:
Facing West, taking a left turn means turning South. The drone flies 20 m South to reach C.
Coordinates of C = (-27, -20)

3. Movement from Waypoint C to Waypoint B:
Facing South, taking a right turn means turning West. The drone flies 27 m West to reach B.
Coordinates of B = (-27 - 27, -20) = (-54, -20)

4. Movement from Waypoint B to Destination A:
Facing West, taking a right turn means turning North. The drone flies 10 m North to land at A.
Coordinates of A = (-54, -20 + 10) = (-54, -10)

Final Direction Analysis:
Destination A is at position (-54, -10) relative to F (0, 0).
Since the x-coordinate is negative (West) and the y-coordinate is negative (South), destination A is located in the South-west direction relative to point F.