Mr. Z is standing facing towards the east. He takes a left turn and walks 5 km to reach point A. Then he takes a left turn and walks 4 km to reach point B. Then he takes a right turn and walks 3 km to reach point C. Then he takes a right turn and walks 10 km to reach point D. In which direction is Mr. Z facing now at point D?
East
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
| Action | Starting Direction | Turn Taken | Facing Direction After Turn |
|---|---|---|---|
| Initial | - | - | East |
| Move to A | East | Left | North |
| Move to B | North | Left | West |
| Move to C | West | Right | North |
| Move to D | North | Right | East |
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.
Important Questions from Direction and Distance
- Vijendra walks a certain distance, say X metres, from his home towards the west. Then he turns left and walks 23 metres. After that, he turns left and walks 36 metres. Then he turns left again to walk 23 metres. He finally turns left and walks 18 metres to reach his home. Find the value of X.
Gaurav exits from the backdoor of his north-facing house and walks 25 m straight, then he takes a left turn and walks 36 m, then he turns left and walks 47 m. He turns left again and walks 36 m. How far and in which direction is he from his house now?
Reeta is standing facing south-east. First, she turns 135° clockwise. After that, she turns 90 ° anticlockwise. Then she turns 45 ° clockwise, followed by a 135 ° anticlockwise turn. In which direction is she facing now?
Sahasra started running from her house towards the north. After 40 meters she turned left and ran for 75 meters. She then turned right and ran for 30 meters, and again turned right to run 75 meters. In which direction was she running finally?
At the time of sunset, Lopa and Kritika are sitting facing each other. If the shadow of Lopa falls to the right of Kritika, in which direction is Kritika facing?
