1. Introduction to Direction Sense Test

Direction Sense Test evaluates a person's ability to determine directions and distances based on given information. It is essential in logical reasoning and competitive exams.

Basic Directions:

• North (↑)
• South (↓)
• East (→)
• West (←)

Intermediate directions: North-East (NE), North-West (NW), South-East (SE), South-West (SW).

2. Key Concepts

• Right Turn: A 90° clockwise turn.
• Left Turn: A 90° counter-clockwise turn.
• Distance: Straight-line or cumulative based on movements.
• Relative Position: Position of one point/person relative to another after movements.

Assume the initial position faces North unless mentioned otherwise.

3. Types of Direction Problems

• Simple Movement: Questions involving basic turns and movements.
• Finding Distance: Calculating the shortest distance between the start and end points.
• Relative Direction: Finding the direction of one point relative to another.
• Complex Movement: A combination of multiple turns and distances.

4. Solving Direction Problems: Step-by-Step Approach

Step 1: Assume the initial direction is North unless specified.
Step 2: Draw a rough diagram of movements on paper.
Step 3: Track turns and distances step-by-step.
Step 4: Calculate the shortest distance using geometry, if required.
Step 5: Identify the final direction or relative position.

5. Example Problems

5.1 Simple Movement

Problem: A person walks 10m North, then 10m East. In which direction is he now from his starting point?

Solution:

• Step 1: Draw the path → 10m North, then 10m East.
• Step 2: The person is in the North-East direction from the starting point.

5.2 Finding Distance

Problem: A person walks 3m North, then 4m East. Find the shortest distance to the starting point.

Solution:

• Draw the path as a right triangle.
• Use Pythagoras Theorem:

$$ Distance = \sqrt{(North)^2 + (East)^2} $$

$$ Distance = \sqrt{(3)^2 + (4)^2} = \sqrt{9 + 16} = 5 \text{ meters} $$

5.3 Complex Movement

Problem: A person walks 10m North, turns right and walks 10m, turns right again and walks 10m. Which direction is he facing now?

Solution:

• Step 1: Start facing North.
• Step 2: Right turn → East.
• Step 3: Second right turn → South.
• Final Direction: South.

6. Direction-Based Shortcuts

• Right Turn: Change direction clockwise (N → E → S → W → N).
• Left Turn: Change direction counter-clockwise (N → W → S → E → N).
• Opposite Directions: North ↔ South, East ↔ West.
• Diagonal Directions: NE ↔ SW, NW ↔ SE.

7. Special Cases

7.1 Opposite Directions

When a person turns two consecutive right or left turns (90° each), the direction becomes opposite:

• Two Right Turns: North → South.
• Two Left Turns: North → South.

7.2 Relative Position

To find the relative position of two points, calculate their horizontal and vertical displacements and determine the direction accordingly.

8. Summary of Key Points

• Right Turn = 90° clockwise.
• Left Turn = 90° counter-clockwise.
• Use Pythagoras Theorem to find the shortest distance.
• Draw a rough diagram to solve complex problems easily.