# Direction Sense — Left, Right, Shadows and Shortest Distance

Source: https://skills101.in/learn/reasoning/direction-sense — Skills101 free tutorial (Logical Reasoning). Updated 2026-11-09.

Direction questions describe a walk and ask where the person ends up, or how far from the start. Draw each step — never solve in your head.

## 1. The compass

![Compass rose with N, E, S, W and NE, NW, SE, SW. A right turn is clockwise, a left turn is anticlockwise](https://skills101.in/learn-img/reasoning/compass.svg)

- Facing **north**: right = east, left = west.
- Facing **south**: right = **west**, left = **east** (it flips!).
- **Right turn = 90° clockwise**, **left turn = 90° anticlockwise**.
- Turning 45° moves you to the in-between direction (north → north-east on a 45° right turn).

> **Trick for turns:** hold your pen on the paper in the direction you face, then rotate it. Your eyes will not lie.

## 2. Draw the walk

![Walking 10 km north, then 15 km east, then 6 km south: the end point is 15 km east and 4 km north of the start, about 15.5 km away](https://skills101.in/learn-img/reasoning/direction-path.svg)

### Example 1
*Ravi walks 10 km north, turns right and walks 15 km, then turns right and walks 6 km. How far is he from the start, and in which direction?*

- After north, a right turn faces **east** (15 km), then another right faces **south** (6 km).
- Net: 15 km east, 10 − 6 = 4 km north.
- Distance = √(15² + 4²) = √241 ≈ **15.5 km**, towards the **north-east**.

### Example 2 — back on the line
*Meena walks 5 km east, turns left and walks 3 km, turns left again and walks 5 km. Where is she from the start?*

East 5 → left = north 3 → left = west 5. East and west cancel → she is **3 km north** of the start.

## 3. Shortest distance = Pythagoras

> **Shortest distance = √(east–west gap² + north–south gap²)**

Learn these triples to skip the square root: **3-4-5, 5-12-13, 8-15-17, 6-8-10, 7-24-25**.

### Example 3
*A car goes 6 km south, then 8 km west. How far is it from the start?* → 6-8-10 triple → **10 km**.

## 4. Shadows

- The sun rises in the **east** → in the **morning**, shadows fall to the **west**.
- The sun sets in the **west** → in the **evening**, shadows fall to the **east**.
- At **noon** there is almost no shadow (in exam questions, assume none).

### Example 4
*One morning, Arjun stood facing a pole. The pole's shadow fell exactly to his right. Which direction was he facing?*

Morning shadow → west. West is on his right → he is facing **south**. (Facing south: right = west ✓)

## Common mistakes

- Forgetting that left and right flip when you face south or west.
- Adding distances instead of using Pythagoras for the straight-line distance.
- Mixing up morning and evening shadows.

## Quick recap

- Draw every step. Right = clockwise, left = anticlockwise.
- Net east–west and net north–south, then Pythagoras.
- Morning shadow → west; evening shadow → east.


Practice quiz and free certificate: https://skills101.in/learn/reasoning/direction-sense