Understanding Direction Changes

The question asks about the starting direction of a man based on his final direction after a series of movements and turns. We are given the sequence of moves and the final direction he is facing.

The sequence of events is:

1. Start walking from a place.
2. Walk 1 kilometer.
3. Turn left.
4. Walk half a kilometer (0.5 km).
5. Turn left again.
6. He is now going eastwards (facing East).

To find the starting direction, it's often easiest to work backward from the final known state.

Working Backwards to Find the Starting Direction

Let's analyze the last step and reverse it:

1. He is currently facing East.

   This is after his second left turn.

2. He turned left just before facing East.

   Turning left means rotating 90 degrees counter-clockwise. If a person turns left and ends up facing East, they must have been facing North before the turn.

   So, before the second left turn, he was facing North.

3. He walked for half a kilometer facing North (before the second turn).

   This happened after his first left turn.

4. He turned left just before walking half a kilometer facing North.

   If a person turns left and ends up facing North, they must have been facing West before that turn (turning left from West leads to North).

   So, just after walking the first kilometer, he was facing West and then turned left to face North.

5. He walked for 1 kilometer and ended up facing West (before the first turn).

   This was his initial movement from the starting place.

   If a person walks 1 kilometer in a certain direction and is then facing West, their starting direction was West.

Therefore, the man started walking towards the West direction.

Verification

Let's check if starting West leads to the final state described:

• Start facing West.
• Walk 1 km West. Still facing West.
• Turn left. Turning left from West makes you face South.
• Walk 0.5 km South. Still facing South.
• Turn left again. Turning left from South makes you face East.

This matches the information given that he is finally going eastwards. The starting direction was indeed West.

The final answer is West.

Revision Table: Directional Changes

Working backwards confirms that the sequence of turns leads to facing East only if the direction before the first left turn was West, meaning the starting direction was West.

Additional Information: Understanding Left and Right Turns

In directional problems, turns are usually 90 degrees. A 'left' turn is a 90-degree turn counter-clockwise, and a 'right' turn is a 90-degree turn clockwise. It's helpful to visualize the directions: North at the top, East to the right, South at the bottom, and West to the left.

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

This knowledge is crucial for solving problems involving directions and turns.