Discussion
I travel 20 miles towards north and then travel 25 miles eastward. I then travel 40 miles rightwards, then travel 30 miles towards right and then travel 12 miles to the left and finally 20 miles northwards. How far am I approximately from my original starting point and in what direction ?
Answer: B
Correct answer: 13 miles towards south-west
Take the start as the origin with east and north positive. North 20 gives \( (0,20) \); east 25 gives \( (25,20) \); facing east, a right turn faces south, so 40 gives \( (25,-20) \); another right turn faces west, so 30 gives \( (-5,-20) \); facing west, a left turn faces south, so 12 gives \( (-5,-32) \); and 20 north gives \( (-5,-12) \). The distance is \[ \sqrt{5^2+12^2} = \sqrt{169} = 13\ \mathrm{miles}, \] and being west and south of the origin, the direction is south-west.
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