How to Solve: CUET Reasoning – Direction Sense and Distance

How to Solve: CUET Reasoning – Direction Sense and Distance

Introduction

"Imagine you’re lost in a city, and your phone dies. The only way to reach your destination? Mastering direction sense and distance—just like the CUET exam will test you. One wrong turn, and you lose marks. Get it right, and you ace the reasoning section."

What You Need To Know First

1. Cardinal Directions (N, S, E, W): Know their positions on a compass.
2. Right vs. Left Turns: A 90° turn changes your direction (e.g., facing North → turning right = East).
3. Basic Distance Units: Meters, kilometers, or steps (CUET uses simple units).

Key Vocabulary

Formulas To Know

1. Pythagorean Theorem (for displacement)
2. Formula: Displacement = √(Horizontal distance² + Vertical distance²)
3. Variables:
   • Horizontal distance = East/West movement.
   • Vertical distance = North/South movement.

4. MEMORISE THIS (not given on exam sheet).

5. Net Direction Calculation

6. Formula: Final Direction = Initial Direction + Turns (Right = +90°, Left = -90°)
7. Example: Facing North (0°), turn right twice → 0° + 90° + 90° = 180° (South).
8. MEMORISE THIS (not given on exam sheet).

Step-by-Step Method

Step 1: Draw a Compass

• Sketch a simple compass (N, S, E, W) on rough paper.
• Mark your starting point (S) and starting direction (e.g., North).

Step 2: List All Movements

• Write down every movement in order:
• Direction (e.g., "Walk 5m East").
• Turns (e.g., "Turn right, walk 3m").

Step 3: Track Direction After Each Turn

• Start with initial direction (e.g., North).
• For each turn:
• Right turn: Rotate 90° clockwise (N → E → S → W → N).
• Left turn: Rotate 90° anti-clockwise (N → W → S → E → N).

Step 4: Calculate Net Displacement

• Separate movements into North-South and East-West.
• Add/subtract distances in each axis:
• North = +, South = –
• East = +, West = –
• Use Pythagoras for straight-line distance (if asked).

Step 5: Find Final Position

• Combine net North-South and East-West distances.
• Example: 3m North + 4m East → Final position = 3m N, 4m E of start.

Step 6: Answer the Question

• Check if the question asks for:
• Final direction (e.g., "Which direction is the person facing?").
• Displacement (straight-line distance).
• Path length (total distance walked).

Worked Example Using Steps

Question: "A person starts walking North for 4m, turns right and walks 3m, then turns left and walks 2m. What is their final position relative to the start?"

Solution: 1. Draw compass: Start at origin (0,0), facing North. 2. List movements:
- Walk 4m North.
- Turn right (now facing East), walk 3m.
- Turn left (now facing North), walk 2m. 3. Track direction:
- Start: North.
- After right turn: East.
- After left turn: North. 4. Calculate net displacement:
- North-South: 4m (North) + 2m (North) = +6m North.
- East-West: 3m (East) = +3m East. 5. Final position: 6m North, 3m East of start. 6. Answer: 6m N, 3m E.

Worked Examples

Example 1 – Basic

Question: "Rohan walks 5m East, then 12m North. What is his displacement from the start?"

Solution: 1. North-South: 12m North. 2. East-West: 5m East. 3. Displacement = √(5² + 12²) = √(25 + 144) = √169 = 13m. Answer: 13m.

What we did and why: - Used Pythagoras because the path forms a right-angled triangle. - Displacement ≠ path length (path = 5 + 12 = 17m).

Example 2 – Medium

Question: "A girl walks 6m South, turns right and walks 8m, then turns right again and walks 10m. How far is she from the start?"

Solution: 1. Start: Facing South. 2. First movement: 6m South. 3. First turn: Right (now facing West), walk 8m West. 4. Second turn: Right (now facing North), walk 10m North. 5. Net displacement:
- North-South: -6m (South) + 10m (North) = +4m North.
- East-West: -8m (West) = -8m East. 6. Displacement = √(4² + 8²) = √(16 + 64) = √80 = 4√5m. Answer: 4√5m.

What we did and why: - Tracked direction after each turn. - Combined movements in the same axis (North-South, East-West).

Example 3 – Exam Style

Question: "A man starts at point A, walks 10m West, then turns 45° to his right and walks 10m. What is his final position relative to A?"

Solution: 1. Start: Facing West. 2. First movement: 10m West. 3. Turn: 45° right (now facing South-West). 4. Second movement: 10m South-West.
- Break into components:
- West: 10 × cos(45°) = 10 × (1/√2) ≈ 7.07m.
- South: 10 × sin(45°) = 10 × (1/√2) ≈ 7.07m. 5. Net displacement:
- West: 10m + 7.07m ≈ 17.07m.
- South: 7.07m. 6. Final position: 17.07m West, 7.07m South of A. Answer: 17.07m W, 7.07m S.

What we did and why: - Recognized a non-90° turn → used trigonometry. - Broke diagonal movement into components.

Common Mistakes

Exam Traps

1-Minute Recap

"Alright, last-minute review for CUET Direction Sense! Here’s the deal: 1. Start with a compass—draw North, South, East, West. 2. Track every movement and turn—right = clockwise, left = anti-clockwise. 3. Separate North-South and East-West distances—add them up. 4. Use Pythagoras for displacement—√(N-S)² + (E-W)². 5. Watch for traps—diagonal moves, final direction vs. position, and multiple turns. 6. Practice 3-4 problems tonight—focus on turns and net displacement. You’ve got this! Now go ace that exam."