Understanding Direction Changes in a Path

This question asks us to determine Mr. Z's final facing direction after a series of turns and movements. To solve this, we need to track his facing direction at each step, as the distances walked do not affect the direction he is facing, only his position.

Step-by-Step Direction Analysis

Let's break down Mr. Z's movement and turns:

• Starting Point: Mr. Z is initially facing towards the East.
• First Turn (to Point A): He takes a left turn.
  • When facing East, a left turn means turning 90 degrees counter-clockwise.
  • This changes his facing direction from East to North.
  • He walks 5 km to reach point A, still facing North.
• Second Turn (to Point B): From point A, he takes another left turn.
  • When facing North, a left turn means turning 90 degrees counter-clockwise.
  • This changes his facing direction from North to West.
  • He walks 4 km to reach point B, still facing West.
• Third Turn (to Point C): From point B, he takes a right turn.
  • When facing West, a right turn means turning 90 degrees clockwise.
  • This changes his facing direction from West to North.
  • He walks 3 km to reach point C, still facing North.
• Fourth Turn (to Point D): From point C, he takes another right turn.
  • When facing North, a right turn means turning 90 degrees clockwise.
  • This changes his facing direction from North to East.
  • He walks 10 km to reach point D, still facing East.

Final Facing Direction at Point D

After following all the turns, we see that at point D, Mr. Z is facing towards the East.

We can summarize the direction changes:

• Start: East
• Left turn: North
• Left turn: West
• Right turn: North
• Right turn: East

Therefore, at point D, Mr. Z is facing East.

Revision Table: Tracking Mr. Z's Direction

Additional Information on Direction and Turns

Understanding how turns affect direction is key in these types of problems. The cardinal directions are North, South, East, and West. They are arranged in a cycle: North → East → South → West → North. Each turn is usually a 90-degree rotation.

• A Left Turn is a 90-degree turn in the counter-clockwise direction.
• A Right Turn is a 90-degree turn in the clockwise direction.

Let's see how this applies to the main directions:

• Facing North: Left is West, Right is East.
• Facing East: Left is North, Right is South.
• Facing South: Left is East, Right is West.
• Facing West: Left is South, Right is North.

The distance covered (5 km, 4 km, 3 km, 10 km) is important for determining the final position but irrelevant for determining the final facing direction.