The three initial and final position of a man on the X-axis are given as
(i) `(-8m, 7m)` (ii) `(7m, -3m)`
(iii) `(-7m, 3m)`
Which pair gives the negative displacement ?

Options

A. (i)
B. (ii)
C. (iii)
D. (i) and (iii)

Explanation

To find which pair of positions gives a negative displacement, we need to calculate the displacement for each pair of initial and final positions. Displacement is defined as the difference between the final position and the initial position.

### Step-by-Step Solution:

1. **Identify the pairs of positions:**
- Pair 1: Initial position = -8m, Final position = 7m
- Pair 2: Initial position = 7m, Final position = -3m
- Pair 3: Initial position = -7m, Final position = 3m

2. **Calculate the displacement for each pair:**

**For Pair 1:**
- Initial position (x₁) = -8m
- Final position (x₂) = 7m
- Displacement (Δx) = x₂ - x₁ = 7m - (-8m) = 7m + 8m = 15m
- Result: Positive displacement (15m)

**For Pair 2:**
- Initial position (x₁) = 7m
- Final position (x₂) = -3m
- Displacement (Δx) = x₂ - x₁ = -3m - 7m = -10m
- Result: Negative displacement (-10m)

**For Pair 3:**
- Initial position (x₁) = -7m
- Final position (x₂) = 3m
- Displacement (Δx) = x₂ - x₁ = 3m - (-7m) = 3m + 7m = 10m
- Result: Positive displacement (10m)

3. **Conclusion:**
- The only pair that gives a negative displacement is Pair 2: (7m, -3m) with a displacement of -10m.

### Final Answer:
The pair that gives the negative displacement is (7m, -3m).

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