Direction and Distance: Turns, Shortest Distance, Shadows and Relative Positions
Direction and Distance: Turns, Shortest Distance, Shadows and Relative Positions
Direction questions are coordinate geometry in plain words. Put the start at the origin, take north as +y and east as +x, and add each leg. The final point gives the shortest distance (Pythagoras), the direction from the start, and the way back. Turns are easiest as compass angles: north 0°, east 90°, south 180°, west 270°.
1. Compass and Turn Rules
| Facing | Right turn (90° clockwise) | Left turn (90° anticlockwise) | About turn (180°) |
|---|---|---|---|
| North | East | West | South |
| East | South | North | West |
| South | West | East | North |
| West | North | South | East |
Angles: N 0°, NE 45°, E 90°, SE 135°, S 180°, SW 225°, W 270°, NW 315°. Clockwise adds, anticlockwise subtracts; wrap round at 360°
Shortest distance from start = √(x² + y²) where x = net east, y = net north
Direction of the end point from the start: signs of (x, y): (+, +) NE, (+, −) SE, (−, −) SW, (−, +) NW; one zero gives a main direction
Way back to the start = the opposite of the end point's direction from the start
| Time | Sun | Shadow falls |
|---|---|---|
| Morning | East | West |
| Evening | West | East |
| Noon | Overhead | No side shadow (used rarely) |
✗ The man ends 3 km north of the start, so he must drive north to return | ✓ To return, he drives 3 km south
✗ Facing north and turning 135° anticlockwise gives south-east | ✓ Anticlockwise from N: NW (45°), W (90°), SW (135°)
हिंदी नोट: दिशा प्रश्नों में आरंभ बिंदु को मूल बिंदु मानिए: उत्तर +y और पूर्व +x। अंतिम बिंदु से सबसे छोटी दूरी √(x² + y²) होती है। सुबह सूर्य पूर्व में होता है और छाया पश्चिम में पड़ती है; शाम को उल्टा।
Exam Pointer: Verified NTPC patterns: turns given in degrees to find the final direction (June 2022 CBT-2), multi-leg drives asking the shortest distance and the direction back to the start (June 2025 Graduate CBT-1 and August 2025 UG CBT-1; this "start at point A" format dominates 2025 papers) and towns placed by direction (June 2025 Graduate CBT-1). Pythagoras distances, direction of the end point and shadow questions had no verified NTPC shift and are tagged syllabus-based.
Pariksha Pattern: Every Way NTPC Asks This Topic
Pattern 1: Turns: final direction faced
[PYQ: NTPC CBT-2 17-Jun-2022 Shift-1]
EXAM LEVEL
Q. Facing north, a man turns right, right again, then left. Which way does he face now?
North → east → south → east.
Answer: East
EXAMATLAS LEVEL
Q. Facing west, a girl turns 45° clockwise, then 180° anticlockwise, then 270° clockwise. Which direction does she face now?
West = 270°. Adding 45° gives 315° (NW); subtracting 180° gives 135° (SE); adding 270° gives 405°, which is 45° (NE).
Answer: North-east
Pattern 2: Multi-leg journey: distance and direction back to the start
[PYQ: NTPC Graduate CBT-1 14-Jun-2025 Shift-1 | NTPC UG CBT-1 7-Aug-2025 Shift-3]
EXAM LEVEL
Q. From point A, a man drives 8 km north, turns right and drives 5 km, turns right and drives 3 km, turns right and drives 5 km, then turns left and drives 2 km. How far and in which direction must he drive to reach A?
East-west: +5 − 5 = 0. North-south: +8 − 3 − 2 = +3. He is 3 km north of A, so he must drive 3 km south.
Answer: 3 km south
EXAMATLAS LEVEL
Q. From point P, a woman walks 15 m east, turns left and walks 9 m, turns left and walks 7 m, turns right and walks 3 m, and turns left and walks 8 m. Find the total distance walked, and how far and in which direction she must walk to return to P.
The legs are E 15, N 9, W 7, N 3, W 8 (a left from north is west, a right from west is north, a left from north is west). Net east = 15 − 7 − 8 = 0 and net north = 12. Total walked = 42 m. She is 12 m north of P, so she walks 12 m south.
Answer: 42 m; 12 m south
Pattern 3: Shortest distance by Pythagoras
[Pattern: syllabus-based, PYQ-style]
EXAM LEVEL
Q. A man walks 6 km east and then 8 km north. How far is he from the start?
√(36 + 64) = 10 km.
Answer: 10 km
EXAMATLAS LEVEL
Q. A boy walks 7 m south, turns left and walks 20 m, turns left and walks 12 m, then turns left and walks 8 m. How far is he from the start, and in which direction?
Legs: S 7, E 20, N 12, W 8. Net east = 12 and net north = 5. Distance = √(144 + 25) = 13 m, and (+, +) means north-east.
Answer: 13 m, north-east
Pattern 4: Direction of the end point from the start
[Pattern: syllabus-based, PYQ-style]
EXAM LEVEL
Q. A woman walks 5 km north and then 5 km east. In which direction is she from her starting point?
Net (+5, +5): north-east.
Answer: North-east
EXAMATLAS LEVEL
Q. Leaving home, Raj walks 4 km west, turns left and walks 3 km, then turns left and walks 8 km. Where is he from home, and how far?
Legs: W 4, S 3, E 8. Net east = 4 and net north = −3, which is south-east. Distance = √(16 + 9) = 5 km.
Answer: 5 km south-east
Pattern 5: Shadows and the sun
[Pattern: syllabus-based, PYQ-style]
EXAM LEVEL
Q. In the morning a man stands facing his own shadow. Which direction is he facing?
The morning sun is in the east, so shadows fall to the west. He faces west.
Answer: West
EXAMATLAS LEVEL
Q. One evening Ravi and Mohan stand facing each other. Ravi's shadow falls exactly to his right. Which direction is Mohan facing?
The evening sun is in the west, so shadows fall east. East is on Ravi's right, so Ravi faces north. Mohan faces Ravi, so Mohan faces south.
Answer: South
Pattern 6: Relative positions of points or towns
[PYQ: NTPC Graduate CBT-1 10-Jun-2025 Shift-1]
EXAM LEVEL
Q. Town B is 4 km east of town A, and town C is 3 km north of B. Where is C with respect to A?
C is at (+4, +3) from A: 5 km away, north-east.
Answer: 5 km north-east
EXAMATLAS LEVEL
Q. P is 6 km north of Q. R is 8 km east of Q. S is 6 km north of R, and T is 4 km west of S. Where is T with respect to P, and how far is R from P?
With Q at (0, 0): P (0, 6), R (8, 0), S (8, 6), T (4, 6). T is 4 km east of P. R to P = √(64 + 36) = 10 km.
Answer: T is 4 km east of P; 10 km
60-Second Revision
- Start at (0, 0): north +y, east +x; add every leg.
- Turns as angles: clockwise adds, anticlockwise subtracts.
- Shortest distance √(x² + y²); the way back is the opposite direction.
- Morning shadow west, evening shadow east.
Next Step: Direction and Distance done. Try the direction set in the ExamAtlas RRB NTPC 2026 mock tests; sketch the legs with arrows and keep a running x and y.