Calculating Distance and Direction: Ritu's Travel Route

This problem involves tracking a person's movement through a series of turns and distances to find their final position relative to their starting point. We need to break down Ritu's journey step by step, considering each direction and distance.

Tracing Ritu's Journey from Point A to Point B

Let's represent Ritu's starting point A as the origin (0, 0) on a coordinate plane, with East being the positive x-axis and North being the positive y-axis. South would be negative y, and West would be negative x.

• Step 1: Ritu starts from point A (0, 0) and drives 9 km towards South.
  New position: (0, -9).
• Step 2: From here, she takes a left turn. Facing South, a left turn is towards the East. She drives 8 km East.
  Movement: +8 km in x-direction.
  New position: (0 + 8, -9) = (8, -9).
• Step 3: She then takes a left turn. Facing East, a left turn is towards the North. She drives 3 km North.
  Movement: +3 km in y-direction.
  New position: (8, -9 + 3) = (8, -6).
• Step 4: She turns left again. Facing North, a left turn is towards the West. She drives 12 km West.
  Movement: -12 km in x-direction.
  New position: (8 - 12, -6) = (-4, -6).
• Step 5: Finally, she takes a right turn. Facing West, a right turn is towards the North. She drives 6 km North and stops at point B.
  Movement: +6 km in y-direction.
  Final position B: (-4, -6 + 6) = (-4, 0).

Determining the Final Position of Point B relative to Point A

Point A was at (0, 0). Point B is at (-4, 0).

The x-coordinate of B is -4. Since the x-axis represents East-West, a negative value means West. The distance in the West direction is 4 km.

The y-coordinate of B is 0. Since the y-axis represents North-South, a value of 0 means B is at the same North-South level as A.

Therefore, Point B is located 4 km towards the West from Point A.

Summary of Displacements:

Let's look at the net displacement in the East-West and North-South directions.

• East-West Movement: +8 km (East) - 12 km (West) = -4 km. The negative sign indicates the net displacement is towards the West. Net displacement West = 4 km.
• North-South Movement: -9 km (South) + 3 km (North) + 6 km (North) = 0 km. The net displacement in the North-South direction is zero.

The final position is 4 km West and 0 km North/South from the start. This confirms that Point B is 4 km towards West from Point A.

Comparing with the Options

Based on our calculation, point B is 4 km towards West from point A.

• Option 1: 4 km towards East (Incorrect)
• Option 2: 2 km towards East (Incorrect)
• Option 3: 4 km towards West (Correct)
• Option 4: 2 km towards West (Incorrect)

The final answer is 4 km towards West.