A puppy was trying to find its mother. It was facing east and walked 10 m. It…
2023
A puppy was trying to find its mother. It was facing east and walked 10 m. It then turned south and walked another 10 m. It then turned north and walked 20 m, then turned west and walked 10 m. Finally, it turned south and walked 2 m. In which direction is it from its original position, and how far?
- A.
60 m north-east
- B.
10 m north-east
- C.
8 m north
- D.
can't be determined
Show answer & explanation
Correct answer: C
Concept: In direction-and-distance problems, resolve every leg of the path onto two independent axes — East-West and North-South. Movements along the same axis in opposite directions cancel out (the net is the difference of the distances), and the net East-West distance together with the net North-South distance fixes the final position relative to the start; the Pythagorean theorem is needed for a diagonal distance only when both axis totals are non-zero.
Working, step by step:
Start at the original point O, facing East, and walk 10 m East (East-West: 10 m East).
Turn South and walk 10 m South (North-South: 10 m South).
Turn North and walk 20 m North (North-South: 20 m North).
Turn West and walk 10 m West (East-West: 10 m West).
Turn South and walk 2 m South (North-South: 2 m South).
Net East-West = 10 m East minus 10 m West = 0. Net North-South = 20 m North minus (10 m South plus 2 m South) = 20 minus 12 = 8 m North.
Cross-check: plot the path on coordinates with East as the positive x-axis and North as the positive y-axis, starting at (0, 0): after step 1, the point is (10, 0); after step 2, (10, -10); after step 3, (10, 10); after step 4, (0, 10); after step 5, (0, 8). The final point (0, 8) confirms zero East-West offset and 8 m of North-South displacement, so the straight-line distance from the start is exactly 8 m due north, with no diagonal component involved.
Result: the puppy ends up 8 m north of its original position.