Direction & Distance

medium importance~1-2 Q in Tier 18 formulas⚡ 6 shortcuts4 subtopics

Every formula in this topic, grouped by subtopic. Print it and pin it above your desk.

Direction conventions and displacement

Shortest distance

d = \sqrt{x^2 + y^2}

x = net East-West move, y = net North-South move, after cancelling.

Number triples

3\text{-}4\text{-}5,\ 5\text{-}12\text{-}13,\ 8\text{-}15\text{-}17,\ 7\text{-}24\text{-}25

Doubles and triples of these also work: 6-8-10, 9-12-15.

Diagonal leg

k\sqrt{2}\ \text{along NE} = k\ \text{North} + k\ \text{East}

The same rule holds for NW, SE and SW.

Clockwise cycle

N \to E \to S \to W \to N

Every right turn moves one step along this circle.

Anticlockwise cycle

N \to W \to S \to E \to N

Every left turn moves one step along this circle.

Reading the end point

(x>0,\ y>0) \Rightarrow \text{North-East}

x is the net East move and y is the net North move. Their signs give the compass word.

Distance between two points

d = \sqrt{(\Delta E)^2 + (\Delta N)^2}

Delta E is the East gap and Delta N is the North gap between the two people.

Distance from speed and time

\text{distance} = \text{speed} \times \text{time}

Use it first when two people walk at different speeds.