7.2 Directions

Why Direction Sense Matters

Direction-sense questions are a staple of the RRB Group D Reasoning section because they test two skills at once — reading comprehension (parsing the movement statements) and spatial reasoning (tracking orientation). The exam expects Class-10 level, so the distances and angles are simple integers, but the chain of statements is deliberately worded to trip up careless readers. A disciplined coordinate-tracking habit turns each question into a routine calculation.

The Eight-Point Compass

The compass has four cardinal directions and four intercardinal (or ordinal) directions, for eight named points total:

The diagram below fixes the rose in memory — the angle between any two neighbouring named points is exactly 45°.

Turn Rules

• Right turn = clockwise = +90° from the current facing direction.
• Left turn = anticlockwise = −90°.
• A half turn (U-turn) = 180° and reverses the facing direction.
• A turn of 45° ("turn towards the right diagonally") moves you from a cardinal to an intercardinal direction (e.g., facing N and turning right 45° → facing NE).

Displacement vs Distance

• Distance travelled is the total path length (sum of every segment walked).
• Displacement is the straight-line distance from start to end, computed by vector addition: combine all North-South movements into one net value, combine all East-West movements into another, then apply Pythagoras.

$\text{Displacement} = \sqrt{(\Delta N)^{2} + (\Delta E)^{2}}$

The bearing (direction of the displacement) is $\tan^{-1}(\Delta E / \Delta N)$, with quadrant adjustments.

Worked Example 1 — Net Displacement

Question: A man walks 3 km North, turns right and walks 4 km, then turns right again and walks 3 km. How far is he from the starting point, and in which direction?

Step 1 — Track facing direction. Start facing North.

• Walks 3 km North → at (0, 3) [taking +y = North, +x = East].
• Turns right (clockwise) from North → now faces East. Walks 4 km → at (4, 3).
• Turns right from East → now faces South. Walks 3 km → at (4, 0).

Step 2 — Net displacement.

$\Delta N = 0$, $\Delta E = 4$. Displacement = $\sqrt{0^{2} + 4^{2}} = 4$ km.

Step 3 — Direction. He is 4 km East of his starting point.

Answer: 4 km, East.

Trap: Many candidates add all three distances (3 + 4 + 3 = 10 km) — that is the distance walked, not the displacement. The question asks "how far is he from the starting point", which always means displacement.

Worked Example 2 — Shadow Direction

Question: At sunrise, a boy is walking facing the sun. After walking 2 km, he turns left and walks 1 km. In which direction is his shadow falling at the end of the walk?

Step 1 — Sun position. At sunrise the sun is in the East. The boy walks facing the sun, so he walks East.

Step 2 — Track facing.

• Walks 2 km East → at (2, 0).
• Turns left (anticlockwise) from East → now faces North. Walks 1 km → at (2, 1).

Step 3 — Time of day is still sunrise. The sun remains in the East, so a shadow falls opposite the sun, i.e. towards the West. The boy's position does not change the shadow's direction — shadows always fall opposite the sun's position. At sunrise, shadows fall west.

Answer: West.

Worked Example 3 — Final Facing Direction

Question: A person is facing North. He turns 135° clockwise, then turns 90° anticlockwise. Which direction is he now facing?

Step 1. Start facing North (0°). Step 2. +135° clockwise → 135° from North = South-East (SE). Step 3. −90° anticlockwise from 135° → 135° − 90° = 45° = North-East (NE).

Answer: North-East.

Quick Reference: Shadow Rules

Exam trap: A question that says "a person walks towards the north and his shadow falls to his right" is really asking about the time of day. Facing North, his right hand points East, so the shadow points East, so the sun must be in the West — it is afternoon or evening. Run the chain in that order (walker's left/right → compass direction of the shadow → opposite direction for the sun → time of day) and these items become one-liners. The mirror case: shadow to his left while walking north means the shadow points West, the sun is in the East, and it is morning.

Worked Example 4 — Combined Distance and Direction

Question: Starting from a point X, a man walks 40 m towards the East, then turns left and walks 30 m, then turns left again and walks 40 m, and finally turns left and walks 30 m to reach point Y. How far is Y from X and in which direction?

Step 1 — Track each leg. Take +y = North, +x = East, start at origin (0, 0).

• Walks 40 m East → (40, 0).
• Turns left (anticlockwise) from East → faces North. Walks 30 m → (40, 30).
• Turns left from North → faces West. Walks 40 m → (0, 30).
• Turns left from West → faces South. Walks 30 m → (0, 0).

Step 2 — Read the end point. He is back at (0, 0), the starting point.

Answer: 0 m — he returns to X. The path traces a 40 × 30 rectangle, and the four legs form a closed loop. RRB uses this rectangle/loop pattern to reward candidates who actually track coordinates rather than add the four distances.

Worked Example 5 — Cardinal-to-Intercardinal Turn

Question: A person is facing West. He turns 45° clockwise, then turns 90° clockwise. Which direction is he now facing?

Step 1. West = 270°. Step 2. +45° clockwise → 315° = North-West (NW). Step 3. +90° clockwise from 315° → 315° + 90° = 405°, subtract 360° → 45° = North-East (NE).

Answer: North-East.

The key skill is keeping angles in the 0–360° range by adding or subtracting 360° whenever you cross 0° or 360°. A clockwise turn adds to the angle; an anticlockwise turn subtracts.

Worked Example 6 — Distance Walked vs Displacement

Question: A girl walks 6 km East, then 8 km North. What is the distance she walked, and what is her displacement from the start?

Distance walked = 6 + 8 = 14 km (the total path length).

Displacement = √(6² + 8²) = √(36 + 64) = √100 = 10 km, in the direction tan⁻¹(8/6) = tan⁻¹(4/3) ≈ 53° North of East, i.e. North-East.

This 6-8-10 Pythagorean triple is an RRB favourite because it gives a clean integer displacement. Memorise the common triples — (3, 4, 5), (5, 12, 13), (6, 8, 10), (8, 15, 17) — so you can compute the displacement without long-division square roots under time pressure.

Worked Example 7 — The Right-Hand Shadow Rule

Question: A person is walking towards the East at 4 PM. Where does his shadow fall relative to him?

Step 1 — Sun position. At 4 PM the sun has crossed the meridian and is in the western half of the sky, so treat the sun as roughly West.

Step 2 — Shadow direction. A shadow always falls opposite the sun, so the shadow points East.

Step 3 — Convert a compass direction into left/right/front/behind. Draw the walker facing East. Then East is in front, West is behind, North is on his left, and South is on his right.

Answer: The shadow falls towards the East — that is, directly in front of him.

Two sanity checks fall out of the same diagram. Walking East in the early morning puts the sun in front of him and the shadow behind. And for the shadow of an East-walker to fall to his right, it would have to point South, which requires the sun to be in the North — so a question that asserts that is almost always a mis-set item, not a puzzle you have solved wrongly. Always do the three steps in order: sun → shadow direction → left/right relative to the walker.

A Tracking Habit That Never Fails

Direction questions become mechanical once you fix two conventions:

1. Always take +x = East, +y = North, origin = start. Every leg's effect is then a sign and a magnitude, never a guess.
2. Always track the facing direction as an angle from North, adding clockwise turns and subtracting anticlockwise turns, wrapping with ±360°.

With these two conventions, the hardest RRB direction question reduces to four numbers added in pairs and one Pythagoras. Practise 20 such questions in a single sitting so the coordinate bookkeeping becomes automatic; under exam time pressure, the candidates who lose marks are those who try to reason "geometrically in their head" and confuse a left turn with a right one.