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.

If waypoint S is located exactly midway between waypoint C and waypoint D, what is the distance and in which direction is waypoint S with respect to destination A?

Correct Answer: The correct option is 27m, east.

Step-by-Step Explanation:

1. Trace the Drone's Path:

Let's represent the locations using standard directional coordinates where East is along the positive x-axis, West is along the negative x-axis, North is along the positive y-axis, and South is along the negative y-axis.

Let distribution center F be at the origin:

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

• The drone flies 27m due west to waypoint D:

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

• Heading west, it makes a left turn (turning south) and flies 20m to waypoint C:

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

• Heading south, it turns right (turning west) and travels 27m to waypoint B:

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

• Heading west, it makes a right turn (turning north) and travels 10m to destination A:

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

2. Determine the Position of Waypoint S:

Waypoint S is located midway between waypoint C (-27, -20) and waypoint D (-27, 0).

The x-coordinate of S is -27.

The y-coordinate of S is the midpoint of 0 and -20:

${\text{y}}_{\text{S}}=\frac{0+(-20)}{2}=-10$

Thus, waypoint S is located at coordinates:

$\text{S}=(-27,-10)$

3. Calculate Distance and Direction of S with respect to A:

Destination A is at (-54, -10) and Waypoint S is at (-27, -10).

Since both point A and point S have the same y-coordinate (-10), point S lies on the same horizontal line as point A.

• Distance:

$\text{Distance}=|-27-(-54\left)\right|=27\text{m}$

• Direction:

Since the x-coordinate of S (-27) is greater than the x-coordinate of A (-54), waypoint S lies to the east of destination A.

Therefore, waypoint S is 27m, east with respect to destination A.