Jamia Millia Islamia MCA Distance And Direction Previous Year Questions (PYQs)
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If you are facing north-east and move 10 m forward, turn left and move 7.5 m, then you are:
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Solution
Facing north-east, your first move of 10 m forward takes you along a line at 45° from north.
Then turning left from north-east → you face north-west direction, and you move 7.5 m.
If you resolve the path:
The first displacement = $(10 \text{m}, 45°)$
⇒ Components: $x_1 = 10\cos45° = 7.07$, $y_1 = 10\sin45° = 7.07$
The second displacement = $(7.5 \text{m}, 135°)$
⇒ Components: $x_2 = 7.5\cos135° = -5.30$, $y_2 = 7.5\sin135° = 5.30$
Net displacement components:
$x = 7.07 - 5.30 = 1.77$, $y = 7.07 + 5.30 = 12.37$
Both $x$ and $y$ are positive ⇒ final position is north-east of initial position.
But since the question asks relative to initial position along main axes,
the major shift is northward.
A man walks $5,\text{km}$ south, turns right and walks $3,\text{km}$, then turns left and walks $5,\text{km}$. In which direction is he from the starting place?
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Solution
Coordinates: $(0,0)!\to!(0,-5)!\to!(-3,-5)!\to!(-3,-10)$, which is to the south-west of the start.
A child’s path: 90 m East → right 20 m (South) → right 30 m (West) → 100 m North.
How far from start did he meet his father?
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Solution
Solution:
Start at (0,0). After moves: (90,0) → (90,−20) → (60,−20) → (60,80).
Distance = √(60²+80²) = √10000 = 100 m.
I am facing South, I turn right and walk 20 m. Then I turn right again and walk 10 m. Then I turn left and walk 10 m and then turning right walk 20 m. Then I turn right again and walk ___ m. In which direction am I from the starting point?”
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Solution
If you are facing north-east and move 10 m forward, turn left and move 7.5 m, then you are:
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Solution
10 m NE ⇒ (7.07 E, 7.07 N). Then 7.5 m to the left of NE (i.e., NW) ⇒ (−5.30 E, +5.30 N).
Net ≈ (1.77 E, 12.37 N): mostly north.
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