Direction Sense — Left, Right, Shadows and Shortest Distance

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

• 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

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.