Directions

Draw it. Put a plus sign on paper and track every turn; right turn = clockwise. Distances are Pythagoras at the end.

Start with this

Draw it. Every direction question is easy on paper and hard in your head.

Directions questions ask where someone ends up, how far from the start, or which way they face. A compass, a few arrows and Pythagoras solve all of them.

Turns and the compass

Worked example

Ravi walks 4 km north, turns right and walks 3 km. How far is he from the start?

1. After the right turn he faces east.
   Why: Right from north is east.
2. He is 4 km north and 3 km east of the start.
   Why: Draw it.
3. √(16 + 9) = 5 km.

Answer: 5

Worked example

A man walks 10 m south, turns left and walks 6 m, turns left and walks 10 m. Where is he from the start?

1. South 10, then left from south = east 6, then left from east = north 10.
   Why: Track the facing direction.
2. The south and north legs cancel: 6 m east of the start.

Answer: 6 m east

Shadows

In the morning the sun is in the east, so shadows fall to the west. In the evening shadows fall to the east. At noon there is almost no shadow.

If a person's shadow falls to his right in the morning, the west is on his right, so he is facing south.

Worked example

In the morning, Asha's shadow falls exactly to her left. Which way is she facing?

1. Morning shadows point west.
   Why: The sun rises in the east.
2. West is on her left.
3. She faces north.

Answer: North

Shortcut: Net displacement

Use it when: Several legs, then 'how far from start'.

1. Add all N-S legs, add all E-W legs separately.
2. Then one Pythagoras.

Net displacement: try it

Walk 3 km N, 4 km E. Distance from start?

1. 3-4-5.

Answer: 5 km

Your turn medium

Ravi walks 10 m north, turns right and walks 6 m, turns right and walks 18 m. How far (m) and which way from start?

1. Net: 6 east, 8 south.
2. √(36 + 64) = 10, towards SE.

Answer: 10 m, south-east

Your turn medium

In the morning, Sita stands facing a pole; the pole's shadow falls to her right. Which way is she facing?

1. Morning shadow points west.
2. West on her right → she faces south.

Answer: South

Your turn medium

A man faces north, turns 90 clockwise, then 180 anticlockwise, then 45 clockwise. Which way does he face?

1. N → E → W → NW.

Answer: North-west

Your turn hard

A goes 4 km south, turns left and walks 3 km, turns left again and walks 8 km. Distance from start?

1. South 4, left = east 3, left = north 8.
2. Net: 3 east, 4 north.
3. 3-4-5 → 5 km, north-east.

Answer: 5 km

Recap

• draw every walk
• turn right = clockwise
• use Pythagoras for the straight-line distance
• use sunrise-east for shadows

Now practise

6 questions with full solutions.

Open practice Back to the lesson