Mr. Oxi starts from Point A and drives 9 km towards the south. He then takes a right turn and drives 3 km, then turns right and drives 15 km. He then takes a right turn and drives 11 km. He takes a final right turn, drives 6 km and stops at Point P. How far (shortest distance) and in which direction should he drive in order to reach Point A again? (All turns are 90-degree turns only unless specified.)

Correct Answer: 8 km to the west

To find the shortest distance and direction Mr. Oxi needs to drive to return to Point A from Point P, let us track his movement step-by-step using a standard 2D Cartesian coordinate system, where Point A is at the origin (0, 0).
Let North be the +y direction, South be the -y direction, East be the +x direction, and West be the -x direction.

Step 1: Track the path taken by Mr. Oxi
1. Start at Point A: Coordinate is (0, 0).
2. Drives 9 km towards South: Moving in the -y direction.
New coordinate = (0, 0 - 9) = (0, -9).
3. Turns Right and drives 3 km: Facing South, a right turn means moving West (-x direction).
New coordinate = (0 - 3, -9) = (-3, -9).
4. Turns Right and drives 15 km: Facing West, a right turn means moving North (+y direction).
New coordinate = (-3, -9 + 15) = (-3, 6).
5. Turns Right and drives 11 km: Facing North, a right turn means moving East (+x direction).
New coordinate = (-3 + 11, 6) = (8, 6).
6. Takes a final Right turn, drives 6 km and stops at Point P: Facing East, a right turn means moving South (-y direction).
Final coordinate at Point P = (8, 6 - 6) = (8, 0).

Step 2: Determine the position of Point P relative to Point A
Point A is located at (0, 0) and Point P is located at (8, 0).
This means Point P is located 8 km directly East of Point A.

Step 3: Determine the distance and direction required to reach Point A from Point P
Since Point P is 8 km to the East of Point A, to go from Point P back to Point A, Mr. Oxi must travel directly West.
Distance required = 8 km - 0 km = 8 km.
Direction required = West.

Therefore, he needs to drive 8 km to the west to reach Point A again.