🧭 Directions & Distance

Day 2 | ⏱️ Part of 3-Hour Reasoning Block | TCS Interview Prep

📌 Subtopics

• Directional Sense (North, South, East, West and diagonals)
• Distance calculation using Pythagorean theorem
• Shadow-based direction problems
• Shortest distance from start to end point
• Left/Right turn based problems

📖 Comprehensive Notes

1. Directional Sense & The Compass

There are 4 main directions (cardinal) and 4 intermediate directions (ordinal):

• Cardinal Directions: North (N), South (S), East (E), West (W).
• Ordinal Directions: North-East (NE), North-West (NW), South-East (SE), South-West (SW).
• Angle spacing: Adjacent cardinal directions are $90^\circ$ apart, while intermediate directions are at a $45^\circ$ angle from cardinal directions.

2. Left and Right Turn Mechanics

Turns are always taken relative to the direction a person is facing:

• Facing North: Left turn goes to West, Right turn goes to East.
• Facing South: Left turn goes to East, Right turn goes to West (opposite of North).
• Facing East: Left turn goes to North, Right turn goes to South.
• Facing West: Left turn goes to South, Right turn goes to North.
• Note: A clockwise (CW) turn of $90^\circ$ is a Right turn. An counter-clockwise (CCW) turn of $90^\circ$ is a Left turn.

Example: A man walks $5\text{ km}$ South, then turns right and walks $3\text{ km}$. In which direction is he walking now? He is walking South. Turning right when facing South means turning West. So, he is walking West.

3. Distance Calculation & Shortest Distance

To find the shortest distance between a starting point and an ending point:

1. Draw a neat coordinate diagram of the path.
2. Form a right-angled triangle where the hypotenuse is the line connecting the start and end points.
3. Apply the Pythagorean Theorem: $\text{Shortest Distance} = \sqrt{(\text{Net Horizontal Distance})^2 + (\text{Net Vertical Distance})^2}$

Example: A person goes $8\text{ m}$ North and then $6\text{ m}$ East. How far is he from his starting point? Net Vertical $= 8\text{ m}$, Net Horizontal $= 6\text{ m}$. $\text{Shortest Distance} = \sqrt{8^2 + 6^2} = \sqrt{64 + 36} = \sqrt{100} = 10\text{ m}$.

4. Shadow-Based Direction Problems

Shadow problems are based on the position of the sun:

• Morning (Sunrise in East):
  • The sun is in the East. All shadows fall to the West.
  • If a person’s shadow falls to their right, they must be facing South.
  • If their shadow falls to their left, they must be facing North.
• Evening (Sunset in West):
  • The sun is in the West. All shadows fall to the East.
  • If a person’s shadow falls to their right, they must be facing North.
  • If their shadow falls to their left, they must be facing South.
• Noon (12:00 PM):
  • The sun is directly overhead. No shadow is formed or it is negligible.

Example: One morning after sunrise, Suresh was standing facing a pole. The shadow of the pole fell exactly to his right. Which direction was Suresh facing? In the morning, shadows fall to the West. The shadow fell to Suresh’s right, which means West is to Suresh’s right. If West is to his right, he must be facing South (since East would be on his left, North behind him).

🌐 Learning Resources

✅ Practice Links

📝 Key Concepts

        North
          |
West ---- + ---- East
          |
        South

Shadow Rules:
  Morning (sunrise in East): Shadow falls to the WEST
  Evening (sunset in West): Shadow falls to the EAST

Shortest Distance: Use Pythagorean theorem
  √(horizontal² + vertical²)

Left Turn from North → West
Right Turn from North → East

🔗 Related Topics

• Geometry Area and Shapes — Calculating coordinate distances (Pythagoras theorem)
• Time Speed and Distance — Tracking routes, speeds, and arrival orientations
• Blood Relations — Integrated relationship-coordinate path problems
• Seating Arrangements and Syllogisms — Knowing directions is key for circular/row arrangements (facing North/South/Center)
• Clocks and Calendars — Angle movements of clock hands are similar to direction turns