Question

Jogi starts from Point A and drives 12 km towards the north. He then takes a left turn, drives 15 km, turns left and drives 13 km. He then takes a left turn and drives 16 km. He takes a final left turn, drives 1 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° turns only unless specified.)

• A. 4 km to the east
• B. 2 km to the west
• C. 7 km to the west
• D. 1 km to the west

Answer 1

Answer:

D. 1 km to the west

Jogi should drive 1 km towards the West to reach Point A again.

Let Point A be the starting point at $(0,0)$:

• North 12 km: Moves to $(0, 12)$

• Left (West) 15 km: Moves to $(-15, 12)$

• Left (South) 13 km: Moves to $(-15, -1)$

• Left (East) 16 km: Moves to $(1, -1)$

• Final Left (North) 1 km: Stops at Point P$(1, 0)$

Final Distance and Direction:

• Point P is exactly 1 km East of Point A.

• Therefore, to return to Point A from P, Jogi must drive 1 km West.