Direction TestPYQ Jan. 21Question 2257 of 165
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Ms. N walks 10\displaystyle 10km towards North from there she walks 6\displaystyle 6km towards South. Then she walks 3\displaystyle 3km towards East. How far and in which direction is she with reference to her starting point?

Options

A4\displaystyle 4 km West
B6\displaystyle 6 km West
C3\displaystyle 3 km East
D5\displaystyle 5 km North/East
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Correct Answer

✅ Option d — 5\displaystyle 5 km North/East

All Options:

  • A4\displaystyle 4 km West
  • B6\displaystyle 6 km West
  • C3\displaystyle 3 km East
  • D5\displaystyle 5 km North/East

Detailed Solution & Explanation

Start at O(0,0)\displaystyle O(0, 0).
1. North 10\displaystyle 10 km →(0,10)\displaystyle \rightarrow (0, 10).
2. South 6\displaystyle 6 km →(0,4)\displaystyle \rightarrow (0, 4).
3. East 3\displaystyle 3 km →(3,4)\displaystyle \rightarrow (3, 4).
Distance =32+42=5\displaystyle = \sqrt{3^2 + 4^2} = 5 km.
Direction from start is North-East (x>0,y>0\displaystyle x > 0, y > 0).
*Discrepancy*: The textbook key lists Option A (4\displaystyle 4 km West), but the correct displacement is 5\displaystyle 5 km North-East (Option D).
Hence, **Option D** is the correct answer.

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