Direction TestMTP June 24 Series IQuestion 2240 of 165
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Sangeeta leaves from her home. She first walk 30\displaystyle 30 metres in North-West direction, and then 30\displaystyle 30m in South-West direction, next she walks 30\displaystyle 30in South-East direction. Finally she turns towards her house. In which direction is she moving?

Options

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

✅ Option b — North-East

All Options:

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

Detailed Solution & Explanation

Let Sangeeta's home be at the origin H(0,0)\displaystyle H(0, 0) on the Cartesian plane, where the positive y\displaystyle y-axis represents North, the negative y\displaystyle y-axis represents South, the positive x\displaystyle x-axis represents East, and the negative x\displaystyle x-axis represents West.
1. **First Movement (North-West)**: She walks 30\displaystyle 30 meters North-West. The vector for this movement is:
v⃗1=−3012i^+3012j^\displaystyle \vec{v}_1 = -30\frac{1}{\sqrt{2}}\hat{i} + 30\frac{1}{\sqrt{2}}\hat{j}
Her position becomes P1=(−152,152)\displaystyle P_1 = (-15\sqrt{2}, 15\sqrt{2}).
2. **Second Movement (South-West)**: From P1\displaystyle P_1, she walks 30\displaystyle 30 meters South-West. The vector for this movement is:
v⃗2=−3012i^−3012j^\displaystyle \vec{v}_2 = -30\frac{1}{\sqrt{2}}\hat{i} - 30\frac{1}{\sqrt{2}}\hat{j}
Her new position is:
P2=P1+v⃗2=(−302,0)\displaystyle P_2 = P_1 + \vec{v}_2 = (-30\sqrt{2}, 0)
3. **Third Movement (South-East)**: From P2\displaystyle P_2, she walks 30\displaystyle 30 meters South-East. The vector for this movement is:
v⃗3=3012i^−3012j^\displaystyle \vec{v}_3 = 30\frac{1}{\sqrt{2}}\hat{i} - 30\frac{1}{\sqrt{2}}\hat{j}
Her new position is:
P3=P2+v⃗3=(−152,−152)\displaystyle P_3 = P_2 + \vec{v}_3 = (-15\sqrt{2}, -15\sqrt{2})
4. **Final Movement (Towards Home)**: Sangeeta now turns and moves towards her home at H(0,0)\displaystyle H(0,0). The vector pointing from her current position P3(−152,−152)\displaystyle P_3(-15\sqrt{2}, -15\sqrt{2}) to her house H(0,0)\displaystyle H(0,0) is:
v⃗home=H−P3=152i^+152j^\displaystyle \vec{v}_{\text{home}} = H - P_3 = 15\sqrt{2}\hat{i} + 15\sqrt{2}\hat{j}
Since both components of this direction vector are positive, she is moving in the North-East direction.

Thus, she is moving in the North-East direction now.
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?

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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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