Alex starts from Point A and drives 8 km towards the east. He then takes a left turn, drives 6 km, turns left and drives 17 km. He then takes a left turn and drives 13 km. He takes a final left turn, drives 9 km and stops at Point P. How far (shortest distance) and towards which direction should he drive in order to reach Point A again? (All turns are 90 degrees turns only, unless specified.)

The correct option is 7 km to the north.

Let us trace Alex's movement step-by-step using a standard 2D Cartesian coordinate system where:

• East corresponds to the positive x-axis (+x)
• West corresponds to the negative x-axis (-x)
• North corresponds to the positive y-axis (+y)
• South corresponds to the negative y-axis (-y)

Step 1: Starting Point
Let Point A be the origin $(0,0)$.

Step 2: First Movement
Alex drives 8 km towards the east.
New position: $(0+8,0)=(8,0)$.
Current facing direction: East.

Step 3: Second Movement
He takes a left turn (turns North) and drives 6 km.
New position: $(8,0+6)=(8,6)$.
Current facing direction: North.

Step 4: Third Movement
He takes a left turn (turns West) and drives 17 km.
New position: $(8-17,6)=(-9,6)$.
Current facing direction: West.

Step 5: Fourth Movement
He takes a left turn (turns South) and drives 13 km.
New position: $(-9,6-13)=(-9,-7)$.
Current facing direction: South.

Step 6: Final Movement to Point P
He takes a final left turn (turns East) and drives 9 km to stop at Point P.
Position of Point P: $(-9+9,-7)=(0,-7)$.

Step 7: Distance and Direction to return to Point A
Point A is located at $(0,0)$ and Point P is located at $(0,-7)$.
To travel from Point P $(0,-7)$ to Point A $(0,0)$:

• The x-coordinates are the same ($0$).
• The change in y-coordinate is $0-(-7)=7$ km in the positive y-direction (North).

Therefore, to reach Point A from Point P, Alex must drive 7 km to the north.