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Turns, Pythagoras & Complex Paths

General Intelligence & Reasoning · Direction Sense

Useful for: SSC CGL

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Overview

Complex direction items chain many turns and distances; disciplined coordinate bookkeeping removes errors.

Key points

Facing update: right = clockwise 90°, left = anticlockwise 90°.
Keep a table: step, facing, move, position.
Distance from start = √(x² + y²); common triples 3-4-5, 5-12-13, 6-8-10.
Direction from start: signs of x (east +) and y (north +).
Angles like "turns 135° clockwise" move to diagonal directions.

Explanation

Diagonal moves split into equal x and y parts (d/√2 each).
If the path returns on itself, cancel opposite moves before calculating.
Questions may ask the direction of the start point from the end point — reverse the signs.
Draw the final triangle to confirm the answer.

Step by step

Track each step.
Find (x, y).
Compute distance and direction.

Examples

Ravi walks 10 km north, turns right and walks 5 km, then turns right and walks 10 km → he is 5 km east of the start.
A person walks 6 km east, 8 km north → 10 km from the start (6-8-10).
Facing east, a man turns 135° anticlockwise → he faces north-west.

Traps and advanced points

Trap: Losing track of facing after several turns.
Trap: Answering the direction of the end from the start when the reverse is asked.
Trap: Using total path length instead of displacement.

Quick revision

Table: facing and position.
Cancel opposite moves.
Reverse signs for "start from end".

Practice MCQs

A man goes 5 km East, 5 km North, 5 km East, 5 km North. Straight distance from start:
1. 5√2 km
2. 10√2 km
3. 10 km
4. 20 km
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Answer: (b) 10√2 km. Total East = 10, total North = 10.
Two friends start from same point. A goes 12 km North, B goes 5 km East. Distance between them:
1. 17 km
2. 7 km
3. 15 km
4. 13 km
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Answer: (d) 13 km. Right angle between North & East.
A cyclist goes 3 km South, 4 km West, 3 km North. His distance from start:
1. 5 km
2. 7 km
3. 4 km
4. 3 km
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Answer: (c) 4 km. South 3 aur North 3 cancel.
If a clock shows 3 o'clock and the hour hand points East, then 6 o'clock direction is:
1. East
2. South
3. North
4. West
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Answer: (b) South. 3 o'clock = East.
A man walks 10 m North, turns right 10 m, turns right 20 m, turns right 10 m. Distance from start:
1. 10 m
2. 0 m
3. 20 m
4. 30 m
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Answer: (a) 10 m. North 10 → East 10 → South 20 → West 10.
Village B is 8 km East of A, C is 6 km North of B. Distance A to C:
1. 2 km
2. 12 km
3. 10 km
4. 14 km
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Answer: (c) 10 km. A to B = 8 (East), B to C = 6 (North), right angle.
Facing South, after turning 135 degrees clockwise a person faces:
1. North-West
2. North-East
3. South-West
4. North
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Answer: (a) North-West. South facing.
A person goes 4 km towards East and turns left and goes 3 km, again turns left goes 4 km. How far from start?
1. 7 km
2. 3 km
3. 5 km
4. 4 km
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Answer: (b) 3 km. East 4 → North 3 → West 4.
The shadow of a tower at sunrise falls exactly on a point. That point is towards which direction from the tower?
1. South
2. West
3. East
4. North
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Answer: (b) West. Sunrise me suraj East me → shadow West me.
A boy runs 20 m South, then 21 m West, then 20 m North. His distance from starting point is:
1. 41 m
2. 29 m
3. 21 m
4. 20 m
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Answer: (c) 21 m. South 20 aur North 20 cancel.
A person walks 55 km east, 4 km north, then 52 km west. How far is the person from the start?
1. 7 km
2. 9 km
3. 5 km
4. 3 km
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Answer: (c) 5 km. Net movement: 3 km east and 4 km north.
A person faces South, walks 71 m straight, then turns left, then right, then left, then left, then left. Final facing direction?
1. West
2. East
3. South
4. North
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Answer: (a) West. Walking straight does not change facing; track each 90° turn on N-E-S-W.
A person faces South, walks 27 m straight, then turns left, then right, then right, then left, then right. Final facing direction?
1. North
2. West
3. South
4. East
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Answer: (b) West. Walking straight does not change facing; track each 90° turn on N-E-S-W.
A person faces East, walks 58 m straight, then turns right, then left, then right, then left, then right. Final facing direction?
1. North
2. South
3. West
4. East
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Answer: (b) South. Walking straight does not change facing; track each 90° turn on N-E-S-W.
A person walks 66 km east, 12 km north, then 61 km west. How far is the person from the start?
1. 13 km
2. 11 km
3. 17 km
4. 15 km
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Answer: (a) 13 km. Net movement: 5 km east and 12 km north.