Path Tracing

Path tracing questions describe a multi-step journey: "Start at A, go 3 km North to B, turn right and go 4 km to C, turn left and go 2 km to D." After following the complete route, you must answer: "What direction is D from A?" or "How far is D from A?" The key skills are (a) keeping track of the current facing direction at every turn and (b) plotting each segment correctly on a rough sketch.

1. Mark the start point on paper with a compass cross nearby (N up, S down, E right, W left).
2. Draw the first segment in the given direction and label its distance.
3. Apply each turn: "turn right" = 90 degrees clockwise from current direction; "turn left" = 90 anti-clockwise.
4. Draw the next segment from the end of the previous one.
5. After all segments, measure or calculate the straight-line distance from start to end and identify the direction.

Example 1: Asha starts facing North. She walks 3 km, turns right, walks 4 km. Where is she relative to her start?

• 3 km North, then turns right = now facing East, walks 4 km East.
• Displacement: 3 North + 4 East → Pythagoras = 5 km, direction = North-East.
• Answer: 5 km North-East of start.

Example 2: Rajan walks 2 km East, turns left, walks 3 km, turns left again, walks 2 km.

• Start East, 2 km East.
• Turn left from East = now facing North. Walk 3 km North.
• Turn left from North = now facing West. Walk 2 km West.
• Net East-West: 2 East - 2 West = 0. Net North-South: 3 North.
• Answer: 3 km North of start.

• "Turn right" while facing South means turning West, not East. The turn is always relative to the current facing direction.
• Not updating the facing direction after each turn — every turn changes what "right" and "left" mean.
• Skipping the sketch: path tracing without a drawing almost always leads to errors.

1. A person walks 5 km North, turns right, walks 5 km, turns right, walks 5 km. How far and in which direction is she from the start?
2. Starting East, after two left turns, which direction are you facing?