Direction & Distance

What you'll learn

• Name and locate all 8 compass directions
• Determine facing direction after clockwise or anticlockwise turns
• Calculate straight-line (displacement) distance using the Pythagorean theorem
• Predict shadow direction based on sun position at different times of day

Key concepts

The 8 Compass Directions

         North (N)
            |
NW ─────────┼───────── NE
            |
West ───────┼─────── East
            |
SW ─────────┼───────── SE
            |
         South (S)

Memory trick: Never Eat Soggy Waffles → N, E, S, W going clockwise.

Turns: Clockwise and Anticlockwise

When a person turns, their new facing direction depends on:

1. The direction they are currently facing
2. The degree of turn (90°, 180°, 270°)
3. Whether the turn is clockwise (right) or anticlockwise (left)

90° turn table (from each starting direction):

Worked Example: A man faces North. He turns 90° clockwise, then 90° anticlockwise.

• North → turn right → East
• East → turn left → North (back to start)

Worked Example 2: A woman faces West. She turns 270° clockwise.

• 270° clockwise = 90° anticlockwise
• West → 90° anticlockwise → South

Tip: 270° clockwise = 90° anticlockwise. 180° clockwise = 180° anticlockwise (same result).

Tracing a Path — Step by Step

Draw a rough sketch for every problem. Mark start, each turn, and each distance walked.

Worked Example: Ravi starts at point A facing North.

• Walks 5 km North → reaches B
• Turns right (East), walks 12 km → reaches C

Final displacement (A to C) = √(5² + 12²) = √(25 + 144) = √169 = 13 km

Direction from A: North-East (moved north then east)

Common right-angle pairs to memorise:

Distance Without a Right Angle

If the path folds back on itself, subtract the return distance.

Worked Example: Priya walks 10 km East, then 4 km West. Net displacement East = 10 − 4 = 6 km East

If she then walks 8 km North: Displacement = √(6² + 8²) = √(36 + 64) = √100 = 10 km from start.

Shadow Direction

The sun's position determines which side shadows fall on.

Worked Example: At 7 a.m., Arun stands and his shadow falls to the West. Which direction is he facing?

• Morning sun is in the East → shadow falls West.
• Shadow always falls directly behind the person relative to the sun.
• Sun is East → shadow is West → Arun's shadow is behind him or in front?
• If shadow is in front of him (to his West side), he is facing West — shadow falls East. Recheck: if shadow falls West, sun is East, so Arun faces East with shadow behind (to his West). He faces East.

Rule: Shadow always falls on the side opposite to the sun. If sun is East → shadow is West.

Quick check

1. A person faces South. He turns 90° clockwise. Which direction is he facing now?
2. Meena walks 6 km North, then 8 km East. How far is she from the starting point?
3. At noon, a boy's shadow falls to his North. Is this possible, and in which hemisphere?
4. A man facing West turns 180°. Then he turns 90° anticlockwise. What direction is he facing?
5. Kiran walks 3 km East, 4 km North, 3 km West. How far is she from the start, and in which direction?

Open the Practice tab for graded questions on Direction and Distance.