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 determine which pair of initial and final positions gives a negative displacement, we will calculate the displacement for each pair using the formula:

\[ \text{Displacement} = \text{Final Position} - \text{Initial Position} \]

Let's analyze each pair step by step.

### Step 1: Calculate Displacement for Pair (i) `(-8m, 7m)`

- **Initial Position**: -8m
- **Final Position**: 7m

Using the formula:
\[ \text{Displacement} = 7m - (-8m) = 7m + 8m = 15m \]

### Step 2: Calculate Displacement for Pair (ii) `(7m, -3m)`

- **Initial Position**: 7m
- **Final Position**: -3m

Using the formula:
\[ \text{Displacement} = -3m - 7m = -10m \]

### Step 3: Calculate Displacement for Pair (iii) `(-7m, 3m)`

- **Initial Position**: -7m
- **Final Position**: 3m

Using the formula:
\[ \text{Displacement} = 3m - (-7m) = 3m + 7m = 10m \]

### Conclusion

From the calculations:
- Pair (i) gives a displacement of **15m** (positive).
- Pair (ii) gives a displacement of **-10m** (negative).
- Pair (iii) gives a displacement of **10m** (positive).

Thus, the pair that gives the negative displacement is **(ii) (7m, -3m)**.

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