Discussion
A man starts from his house, walks for 5 meters towards East, then turns to the North and walks 10 meters again; then he turns towards East and again walks 5 meters. If his house faces to the North, in which direction he is from the starting point?
Answer: B
He is North-East of the starting point.
Track the moves on a grid with East as +x and North as +y: 5 m East takes him to (5, 0), 10 m North to (5, 10), and 5 m East to (10, 10).
His final position is 10 m East and 10 m North of the start, so the direction from the starting point is North-East, at a distance of \(10\sqrt{2} \approx 14.1\) m. The fact that his house faces North is a distractor: it says nothing about the direction of his displacement. North-West and South-East point the wrong way on one axis, and plain North ignores the 10 m he went East.
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