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.

Let us analyze the step-by-step path of the automated delivery drone starting from distribution center F, setting up a standard Cartesian coordinate system where:

• East represents the positive x-direction (+x)
• West represents the negative x-direction (-x)
• North represents the positive y-direction (+y)
• South represents the negative y-direction (-y)

Let the initial departure point F be at the origin:

$\text{F}=(0,0)$

Step 1: Movement from F to Waypoint D
The drone departs from F and flies due West for 27m to reach waypoint D.
Moving West decreases the x-coordinate by 27m.
Coordinates of D:

$\text{D}=(-27,0)$

Step 2: Movement from Waypoint D to Waypoint C
Facing West, making a left turn means turning South.
The drone flies South for 20m to reach waypoint C.
Moving South decreases the y-coordinate by 20m.
Coordinates of C:

$\text{C}=(-27,-20)$

Step 3: Movement from Waypoint C to Waypoint B
Facing South, making a right turn means turning West.
The drone flies West for 27m to reach waypoint B.
Moving West decreases the x-coordinate by an additional 27m.
Coordinates of B:

$\text{B}=(-27-27,-20)=(-54,-20)$

Step 4: Movement from Waypoint B to Destination A
Facing West, making a right turn means turning North.
The drone travels North for 10m to land at destination A.
Moving North increases the y-coordinate by 10m.
Coordinates of A:

$\text{A}=(-54,-20+10)=(-54,-10)$

Final Direction Determination:
Destination A has coordinates $(-54,-10)$ relative to the origin F $(0,0)$.
Since the x-coordinate is negative (-54m), destination A lies to the West of F.
Since the y-coordinate is negative (-10m), destination A lies to the South of F.

Therefore, the direction of destination A with respect to initial departure point F is South-west.