Direction Sense • Topic 2 of 4

Net Displacement (Pythagoras)

Add up movement along the East-West axis and along the North-South axis separately (opposite directions cancel). The straight-line distance from start to finish is √(EW² + NS²).

Net distance = the hypotenuse

Walk 3 km East then 4 km North. The two legs are at right angles, so the start-to-finish distance is the hypotenuse of a right triangle:

3 km East 4 km North 5 km start end
√(3² + 4²) = √25 = 5 km. The legs form a 3-4-5 right triangle.
Cancel first, then Pythagoras. If a path goes 5 km East and later 2 km West, the net East-West is 3 km. Net up the two axes separately, then take √(EW² + NS²). SSC picks numbers that form clean triples: 3-4-5, 6-8-10, 5-12-13.

✅ Solved examples

1. Walk 3 km East, then 4 km North. Distance from start?
√(3² + 4²) = √25 = 5 km.
2. Walk 6 km North, then 8 km East. Distance from start?
√(36 + 64) = √100 = 10 km.
3. Walk 5 km East, then 5 km West. Distance from start?
They cancel: 0 km.
4. Walk 4 km East, 3 km North, 4 km West. Distance from start?
EW nets to 0, NS = 3 → 3 km North.

✏️ Practice — try these, take hints as needed

1. 9 km East, 12 km North. Distance?
√(81+144).
√225.
—
15 km
2. 8 km South, 6 km East. Distance?
√(64+36).
—
—
10 km
3. 7 km North, 7 km South. Distance?
Cancel.
—
—
0 km
4. 3 km West, 4 km South. Distance?
√(9+16).
—
—
5 km
5. 10 km East, 10 km West, 5 km North. Distance?
EW cancels.
—
—
5 km

📝 Topic test — 8 questions

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