DIRECTION AND DISTANCE REASONING

 📘 Chapter: Direction and Distance – Reasoning

🔶 Objective:

To test a candidate’s ability to interpret and analyze movements in different directions and calculate the distance and final position with respect to a starting point.

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✅ Key Concepts Covered:

1. Main Directions:

There are four cardinal directions:

• North (N)

• South (S)

• East (E)

• West (W)

And four intermediate (ordinal) directions:

• North-East (NE)

• North-West (NW)

• South-East (SE)

• South-West (SW)

🔺 Tip: East is to your right when facing North.

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2. Turning and Movement:

When a person or object moves in a particular direction and takes turns (left/right), the new direction is determined as follows:

Facing	Turn Left	Turn Right
North	West	East
South	East	West
East	North	South
West	South	North

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3. Distance Calculation:

• Use the Pythagoras Theorem to calculate the shortest distance (straight line or displacement):

  $$\text{Distance} = \sqrt{(x^2 + y^2)}$$

• Common when movement is in perpendicular directions (e.g., North, then East).

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4. Relative Direction:

Understanding how the direction changes when the orientation of the person is changed. For instance:

• If facing East, and asked what lies to the left: it is North.

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🔹 Types of Questions Asked:

1. Basic Movement:

Simple walk-based questions involving a few steps in different directions.

Example:

A walks 5 km North, then 3 km East. What is the final position?

Solution:

• Displacement: $\sqrt{5^2 + 3^2} = \sqrt{34} \approx 5.83$ km

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2. Direction-Based (Final Facing Direction):

Example:

A man walks 10 km South, turns left, walks 5 km. Which direction is he facing?

Solution:

• South → Left = East

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3. Distance Between Start and End Point:

Asked after multiple movements. Often involves 90° or 45° angles.

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4. Shadow-Based Questions:

Used to determine direction based on time and position of shadows.

Concept:

• Morning: Sun rises in East, shadows fall in West

• Evening: Sun sets in West, shadows fall in East

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5. Complex Puzzles:

Multiple turns and movements, and often involve multiple people. Diagrams are useful here.

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📊 Strategies to Solve:

1. Draw a rough sketch based on directions and distances.

2. Mark turns and direction changes carefully.

3. Use standard directional arrows: ↑N, ↓S, →E, ←W

4. Use coordinate-based logic for complex problems.

5. Learn common right-angle triangle values:
   3-4-5, 5-12-13, 6-8-10

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✏️ Common Errors to Avoid:

• Confusing left/right turn relative to the current direction.

• Misinterpreting shadow-based questions.

• Failing to apply Pythagoras Theorem correctly.

• Not updating the direction after every turn.

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📚 Practice Tip:

Do 10–15 questions a day from various levels – start with direct movement and then practice puzzles with multiple turns and angles. Time yourself to build speed and accuracy.