Satish starts from Point Y and drives 19 km towards west. He then takes a right turn, drives 10 km. He then turns right and drives 11 km. He takes a final right turn, drives 10 km and stops at Point Z. How far (shortest distance) and towards which direction should he drive in order to reach Point Y again? (All turns are 90° turns only unless specified.)

Correct Answer: 8 km towards east

Step-by-step Explanation:

Let us track Satish's movement step-by-step starting from Point Y on a 2D Cartesian plane where West is along the negative x-direction, East is along the positive x-direction, North is along the positive y-direction, and South is along the negative y-direction.

Step 1: Initial position and first movement
Satish starts at Point Y. Let us assign coordinates to Point Y as $(0,0)$.
He drives 19 km towards the West.
His new position becomes $(-19,0)$.

Step 2: Second movement
Facing West, he takes a right turn (which points towards North) and drives 10 km.
His new position becomes $(-19,10)$.

Step 3: Third movement
Facing North, he turns right (which points towards East) and drives 11 km.
His new position becomes:

$(-19+11,10)=(-8,10)$

Step 4: Final movement to Point Z
Facing East, he takes a final right turn (which points towards South) and drives 10 km to stop at Point Z.
His final position at Point Z is:

$(-8,10-10)=(-8,0)$

Step 5: Determining the distance and direction to reach Point Y from Point Z
Point Z is located at $(-8,0)$ and Point Y is located at $(0,0)$.
The distance between Point Z and Point Y is:

$0-(-8)=8\text{km}$

Since Point Z is 8 km to the West of Point Y, Satish needs to drive 8 km towards East to reach Point Y again.