Direction Test — Study Notes
Overview
Direction Test is a core reasoning topic in the Maharashtra Police Bharti exam that evaluates your ability to track movement and determine final positions or distances. These problems simulate real-world navigation scenarios — essential skills for police personnel who must mentally map locations during patrolling, pursuit, or crime scene analysis.
This topic carries moderate weightage but offers quick marks once you master the basic framework. Questions typically involve a person walking in various directions, and you must find either the final direction faced, straight-line distance from the starting point, or the direction of a point relative to another. The key is building a strong mental compass and applying Pythagoras theorem for distance calculations.
Students who develop a habit of drawing quick diagrams consistently score full marks here. The topic connects well with Blood Relations (combined direction-relation problems) and requires basic geometry understanding.
Key Concepts
- Eight Cardinal & Ordinal Directions: North (N), South (S), East (E), West (W) are cardinal. North-East (NE), North-West (NW), South-East (SE), South-West (SW) are ordinal/intermediate — positioned at 45° between cardinals.
- Clockwise Turn Order: N → NE → E → SE → S → SW → W → NW → N. A 90° clockwise turn from North gives East; anticlockwise gives West.
- Left and Right Depend on Current Facing: "Turn right" means 90° clockwise from your current direction; "turn left" means 90° anticlockwise. If facing South, turning right makes you face West.
- Opposite Directions: N↔S, E↔W, NE↔SW, NW↔SE. If someone faces North and turns 180°, they now face South.
- Shadow and Sun Rules: Morning sun rises in East, so shadow falls West. Evening sun sets in West, so shadow falls East. At noon (overhead sun), shadow is minimal/directly below.
- Pythagoras for Straight-Line Distance: When movements form a right angle, final distance from start = √(horizontal² + vertical²).
- Net Displacement Method: Add all North movements, subtract all South movements to get net vertical. Similarly for East-West to get net horizontal. Then apply Pythagoras.
Formulas / Key Facts
Direction Angles:
- Each cardinal direction is 90° apart
- Each ordinal direction is 45° from adjacent cardinals
- Full rotation = 360°
Turn Calculations:
- 90° right from N = E
- 90° left from N = W
- 180° from any direction = opposite direction
- 270° right = 90° left (same result)
Distance Formula:
- Straight-line distance = √(net East-West distance)² + (net North-South distance)²
Shadow Rules:
- 6 AM: Sun in East → Shadow towards West
- 6 PM: Sun in West → Shadow towards East
- 12 Noon: Sun overhead → No shadow / very short
Quick Angle Reference:
- 45° turn from N (clockwise) = NE
- 135° turn from N (clockwise) = SE
- One full turn (360°) = original direction
Worked Examples
Example 1: Final Direction
Problem: Ramesh starts facing North. He turns 90° clockwise, then 180°, then 90° anticlockwise. Which direction is he facing now?
Solution:
- Start: North
- 90° clockwise: North → East
- 180° turn: East → West
- 90° anticlockwise: West → South
Answer: South
Example 2: Distance from Starting Point
Problem: A man walks 8 km North, then 6 km East. How far is he from the starting point?
Solution:
- Movement forms a right angle (North then East)
- Distance = √(8² + 6²) = √(64 + 36) = √100 = 10 km
Answer: 10 km
Example 3: Complex Movement
Problem: Priya walks 5 km South, then 3 km East, then 2 km North, then 3 km West. How far and in which direction is she from the start?
Solution:
- Net North-South: 5 km South − 2 km North = 3 km South
- Net East-West: 3 km East − 3 km West = 0 km
- She is exactly 3 km South of starting point
Answer: 3 km South
Example 4: Shadow-Based Direction
Problem: One morning, Sunil was walking. His shadow fell to his left. Which direction was he facing?
Solution:
- Morning sun is in the East
- Shadow falls opposite to sun, i.e., towards West
- If shadow is to his left, West is on his left
- Therefore, he is facing South
Answer: South
Common Mistakes
- Confusing left/right with fixed directions → Left and right are relative to the person's current facing direction, not the diagram. Always update the facing direction after each turn before applying the next instruction.
- Forgetting to convert 270° turn → A 270° clockwise turn equals 90° anticlockwise. Students often miscalculate large angles. Remember: 270° right = 90° left.
- Ignoring net displacement → When movements include opposite directions (North then South), students calculate total distance walked instead of net displacement. Always subtract opposite movements.
- Wrong Pythagoras application → Students apply Pythagoras when movements are in the same line. Use Pythagoras only when final net movements are perpendicular (one horizontal, one vertical).
- Shadow direction error in morning vs evening → Mixing up that shadow falls opposite to the sun. Create a mental image: face the sun, your shadow is behind you.
- Not drawing diagrams → Attempting to solve mentally leads to errors. Always draw a quick cross (+) representing N-S-E-W and trace the path.
Quick Reference
- Clockwise from North: N → E → S → W → N (90° each step)
- Opposite pairs: N↔S, E↔W, NE↔SW, NW↔SE
- Right turn = clockwise 90°; Left turn = anticlockwise 90°
- Morning shadow = West; Evening shadow = East
- Distance from start = √(net vertical)² + (net horizontal)²
- Always draw a diagram — mark starting point, trace each movement, mark final point