Direction TestMTP March 22Question 2232 of 165
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A boy from his home, first walks 20 m in North-West direction then 20 m in South - West direction. Next, he walks 20m South - East direction. Finally, he turns towards his house. In which direction is he moving?

Options

ANorth - West
BNorth - East
CSouth - West
DSouth - East
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Correct Answer

✅ Option b — North - East

All Options:

  • ANorth - West
  • BNorth - East
  • CSouth - West
  • DSouth - East

Detailed Solution & Explanation

Let the boy's home be at the origin H(0,0)\displaystyle H(0, 0) on the Cartesian coordinate plane.
1. **First Movement (North-West)**: He walks 20\displaystyle 20 meters North-West. The vector for this movement is:
v⃗1=−2012i^+2012j^\displaystyle \vec{v}_1 = -20\frac{1}{\sqrt{2}}\hat{i} + 20\frac{1}{\sqrt{2}}\hat{j}
His coordinates become P1=(−102,102)\displaystyle P_1 = (-10\sqrt{2}, 10\sqrt{2}).
2. **Second Movement (South-West)**: From P1\displaystyle P_1, he walks 20\displaystyle 20 meters South-West. The vector for this movement is:
v⃗2=−2012i^−2012j^\displaystyle \vec{v}_2 = -20\frac{1}{\sqrt{2}}\hat{i} - 20\frac{1}{\sqrt{2}}\hat{j}
His coordinates become:
P2=P1+v⃗2=(−202,0)\displaystyle P_2 = P_1 + \vec{v}_2 = (-20\sqrt{2}, 0)
3. **Third Movement (South-East)**: From P2\displaystyle P_2, he walks 20\displaystyle 20 meters South-East. The vector for this movement is:
v⃗3=2012i^−2012j^\displaystyle \vec{v}_3 = 20\frac{1}{\sqrt{2}}\hat{i} - 20\frac{1}{\sqrt{2}}\hat{j}
His coordinates become:
P3=P2+v⃗3=(−102,−102)\displaystyle P_3 = P_2 + \vec{v}_3 = (-10\sqrt{2}, -10\sqrt{2})
4. **Final Movement (Towards Home)**: He turns and moves towards his home at H(0,0)\displaystyle H(0,0). The vector pointing from his current position P3(−102,−102)\displaystyle P_3(-10\sqrt{2}, -10\sqrt{2}) to his house H(0,0)\displaystyle H(0,0) is:
v⃗home=H−P3=102i^+102j^\displaystyle \vec{v}_{\text{home}} = H - P_3 = 10\sqrt{2}\hat{i} + 10\sqrt{2}\hat{j}
Since both components of this vector are positive, he is moving in the North-East direction.

**Note on Typographical Error**: The textbook answer key incorrectly lists Option D (South-East) as the correct answer. As mathematically proven above, to return home from his final position, the boy must move in the North-East direction. Therefore, North-East (Option B) is the mathematically correct answer.
Hence, **Option B** is the correct answer.

More Questions from Direction Test

A man stands on a point and starts walking towards North then turns left then turns right and then left in which direction he is moving.

Rahim started from point X and walked straight 5\displaystyle 5 km west, then turned left and walked straight 2\displaystyle 2 km, then again turned left and walked straight 7\displaystyle 7 km. In which direction is he from the point X?

Manu wants to go to the market. He starts from his house towards North and reaches a crossroad after 30\displaystyle 30m. He turns towards East, goes 10\displaystyle 10m till the second crossing and turns again, moves towards South straight for 30\displaystyle 30m where marketing complex exits. In which direction is the market from his house?

A man is facing North-West. He turns 90° in the clockwise direction, then 180° in the anticlockwise direction and then another 90° in the same direction. Which direction is he facing now?

Rajni walked 20 m towards the North. Then she turned right and walks 30 m. Then she turns right and walks 35 m. Then she turns left and walks 15 m. Finally she turns left and walks 15 m. In which direction and how many meters is she from the starting position?

At a crossing, there was a direction pole, which was showing all the four correct directions. But due to the wind, it turns in such a manner that now West pointer is showing South. Harish went in the wrong direction thinking that he was travelling East. In which direction he was actually travelling?

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