Manish starts from Point A and drives 12 km towards East. He then takes a left turn, drives 5 km, turns left and drives 30 km. He then takes a left turn and drives 20 km. He takes a final left turn, drives 18 km and stops at Point Q. How far (shortest distance) and towards which direction should he now drive to reach Point A again? (All turns are 90° turns only.)
10 km towards South
15 km towards North
10 km towards North
15 km towards South
15 km towards North
The correct option is 15 km towards North.
Let us analyze the step-by-step movement of Manish starting from Point A on a standard 2D Cartesian coordinate plane where Point A is at the origin .
Step 1: Start at Point A
Initial coordinates:
Step 2: Drives 12 km towards East
Moving East increases the x-coordinate by 12 km.
New position:
Step 3: Takes a left turn and drives 5 km
Facing East, a left turn means driving North, which increases the y-coordinate by 5 km.
New position:
Step 4: Takes a left turn and drives 30 km
Facing North, a left turn means driving West, which decreases the x-coordinate by 30 km.
New position:
Step 5: Takes a left turn and drives 20 km
Facing West, a left turn means driving South, which decreases the y-coordinate by 20 km.
New position:
Step 6: Takes a final left turn, drives 18 km and stops at Point Q
Facing South, a left turn means driving East, which increases the x-coordinate by 18 km.
Coordinates of Point Q:
Finding the distance and direction to reach Point A from Point Q:
Point A is at and Point Q is at .
The difference in x-coordinates is 0 km.
The difference in y-coordinates is:
Since Point Q is directly below (South of) Point A by 15 km, Manish needs to drive 15 km towards North to reach Point A again.