Direction

Direction

🟢 Lite — Quick Review (1h–1d)

Core Definition: Direction problems track position and orientation using cardinal (N,S,E,W) and ordinal (NE,SE,SW,NW) directions with turns.

Key Formulas:

• 360° = full circle; 90° between adjacent cardinals; 45° between cardinal and ordinal
• Displacement = √(NetEast² + NetNorth²)
• NetEast = East moves − West moves; NetNorth = North moves − South moves
• Opposite direction: add 180° to bearing

Must-Know Rules:

• Left turn = counterclockwise; Right turn = clockwise
• Shadow falls opposite the sun (sun in East → shadow West)
• Multiple moves: add vectors, not distances

Exam Pointers (CAT):

1. 2-4 questions per DILR slot; often in LR section
2. Common trap: taking left/right relative to map instead of current facing
3. Always re-evaluate your position after each move

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🟡 Standard — Regular Study (2d–2mo)

Cardinal and Ordinal System

The compass uses 4 cardinal directions (N, E, S, W) and 4 ordinal directions (NE, SE, SW, NW) positioned 45° apart. The right-hand rule arranges them clockwise: N → NE → E → SE → S → SW → W → NW → N. A bearing is the clockwise angle measured from North (0°), so East = 90°, South = 180°, West = 270°. A bearing of 225° points to SW (between S and W).

Turn Mechanics

A left turn is 90° counterclockwise; a right turn is 90° clockwise. If you face East and turn right, you face South. Turn left from East → North. From West, turn right → North. A 180° turn reverses direction completely (North → South). Each turn updates your facing direction for the next move.

Displacement Calculation

Walking 3 km East, then 4 km North: net displacement = √(3² + 4²) = 5 km. Use Pythagorean theorem for perpendicular moves. NetEast = sum of all East/West components; NetNorth = sum of all North/South components.

Shadow Problems

The sun rises in East and sets in West. A shadow falls opposite the sun. Morning sun = shadow points West. Evening sun = shadow points East.

Common Errors

1. Treating “left” as absolute map direction rather than relative to current facing
2. Adding distances when returning along same path (should subtract)
3. Forgetting to update facing direction after each turn

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🔴 Extended — Deep Study (3mo+)

Advanced Turn Sequences

Complex problems require tracking position and orientation after every move. Example: start East, move 10m, turn right (face South), move 10m, turn left (face East), move 10m. Final position: 20m East of start. Pattern: alternating L/R turns cancel perpendicular movement.

Bearing and Opposite Directions

Bearing quantifies direction as clockwise angle from North. Opposite directions differ by 180°. From bearing A, the opposite bearing = (A + 180°) mod 360°. A bearing of 250° has opposite at 70° (or S70°W).

Vector Addition for Net Displacement

When moves are not perpendicular, break each move into components:

• North component = d × cos(θ), where θ is angle from North
• East component = d × sin(θ)

Then sum all North components and all East components separately. Displacement magnitude = √(ΣN² + ΣE²).

Ordinal Direction Precision

NORTHEAST (45°) is exactly halfway between North and East. The 8-point compass divides the circle into 45° segments. Facing an ordinal (NE), a 90° right turn → SE. Facing SW, a 90° left turn → SE.

Man-Soldier Rule (Left-Hand Rule)

Hold the map in your left hand. Your direction of travel aligns with the map’s orientation. Left and right turns are determined by your current facing, not by the map.

Practice Prompts

1. A person starts at origin, walks 20m North, turns right (East), walks 15m, turns left (North), walks 10m, turns left (West), walks 15m. Where are they? Calculate displacement from start.
2. In a race, R runs 3km South, then turns left (East) for 4km, then turns left (North) for 3km. The finish point is 4km East of the start. Is this true or false? Verify using vector addition.

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