This problem involves calculating the shortest distance and direction required to return to the starting point after a series of movements. We can solve this by tracking the position using a coordinate system.

Movement Tracking

Let's assume the starting Point A is at the origin (0, 0) of a coordinate plane, where North corresponds to the positive y-axis and East corresponds to the positive x-axis.

The movements are as follows:

• Starts at A (0, 0).
• Drives 5 km towards the north. New position: (0, 5).
• Takes a right turn (now facing East) and drives 2 km. New position: (0+2, 5) = (2, 5).
• Turns right (now facing South) and drives 9 km. New position: (2, 5-9) = (2, -4).
• Turns right (now facing West) and drives 7 km. New position: (2-7, -4) = (-5, -4).
• Takes a final right turn (now facing North) and drives 4 km. New position: (-5, -4+4) = (-5, 0).
• Stops at Point P (-5, 0).

Final Position Calculation

The final position, Point P, is located at coordinates (-5, 0).

Distance and Direction Calculation

We need to find the shortest distance and direction from Point P (-5, 0) back to Point A (0, 0).

• Horizontal Displacement: The change in the x-coordinate is $0 - (-5) = +5$ km. A positive change in x means movement towards the East.
• Vertical Displacement: The change in the y-coordinate is $0 - 0 = 0$ km. There is no net change in the North-South direction.

The shortest distance can be calculated using the distance formula, which is equivalent to finding the magnitude of the displacement vector:

Distance $= \sqrt{(\Delta x)^2 + (\Delta y)^2} = \sqrt{(5)^2 + (0)^2} = \sqrt{25} = 5$ km.

Since the displacement is entirely along the positive x-axis (+5 km), the direction needed to travel from Point P to Point A is East.

Therefore, one needs to drive 5 km to the east to reach Point A again from Point P.