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Bunuel
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IanStewart
I wouldn't actually use a coordinate plane to solve the question, but using one (labeled in miles) makes it easier to explain the solution. If we imagine the driver starts at (0, 0), after then going 14 miles west, he will be at (-14, 0), after then going 7 miles north he will be at (-14, 7), after then going 9 miles east he will be at (-5, 7), and after going 19 miles south he will be at (-5, -12). The distance from that point to (0, 0) is 13 miles (because we get a 5-12-13 triangle) so 13 is the answer.

How would you approach it instead? Just keep track of the distances and the directions traveled?
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Bunuel
On a certain day, a delivery driver must make 4 deliveries. He departs from the dispatch office and travels 14 miles due west to his first delivery. From there, his second delivery is 7 miles due north, and his third delivery is 9 miles due east of the location of his second delivery. His last delivery is 19 miles due south of his third. Assuming the terrain is flat, what is the distance, in miles, that the driver must travel to return to the dispatch office, if he travels in a straight line via the shortest route?

A. 33
B. 17
C. 13
D. 7
E. It cannot be determined from the information given.
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\(=\sqrt{5^2+12^2} = 13\), Answer will be (C)
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landwe12321
How would you approach it instead? Just keep track of the distances and the directions traveled?

Yes -- it's not really different from what I explained, conceptually, but there's no need to explicitly use a coordinate plane. And if you also notice that the sequence of the deliveries doesn't matter, you can just combine the east and west deliveries first, and then the north and south ones, and see where the driver ends up that way (possibly without even writing anything down) -- he'll be 5 miles west and 12 miles south, from which we get a 5-12-13 triangle and a straight-line distance of 13 miles.
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