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 Option: 27m, east

Let us trace the drone's movement step-by-step using a standard 2D Cartesian coordinate system, setting the starting distribution center F at the origin (0, 0).

standard directional directions:

• East = +x direction
• West = -x direction
• North = +y direction
• South = -y direction

Step 1: Locate Waypoints and Destination

1. Distribution Center F:

$F=(0,0)$

2. Waypoint D: Drone flies due west for 27m from F.

$D=(-27,0)$

3. Waypoint C: Facing west, a left turn points south. Flying 20m south from D:

$C=(-27,-20)$

4. Waypoint B: Facing south, a right turn points west. Flying 27m west from C:

$B=(-27-27,-20)=(-54,-20)$

5. Destination A: Facing west, a right turn points north. Flying 10m north from B:

$A=(-54,-20+10)=(-54,-10)$

Step 2: Find the Position of Waypoint S

Waypoint S is located exactly midway between C(-27, -20) and D(-27, 0). Using the midpoint formula:

$S=(\frac{-27+(-27)}{2},\frac{-20+0}{2})=(-27,-10)$

Step 3: Determine Distance and Direction of S with respect to A

We compare the coordinates of Waypoint S(-27, -10) with respect to Destination A(-54, -10):

• Both A and S have the exact same y-coordinate (-10), which means S is along the same horizontal line as A.

• The x-coordinate of S (-27) is greater than the x-coordinate of A (-54) by:

$-27-(-54)=27\text{meters}$

Since the x-coordinate of S is to the right (+ direction) of A, waypoint S is located 27m east with respect to destination A.