State the co-ordinates of the following points under reflection in x-axis :
(i) (3,-2) (ii) (-5,4) (iii) (0,0)

Answer

To find the coordinates of the given points under reflection in the x-axis, we will follow these steps:

### Step-by-Step Solution:

1. **Understanding Reflection in the x-axis**:
- When a point (x, y) is reflected in the x-axis, the x-coordinate remains the same, while the y-coordinate changes its sign. Thus, the reflection of (x, y) in the x-axis is (x, -y).

2. **Reflecting the first point (3, -2)**:
- Original point: (3, -2)
- Applying the reflection rule:
- x-coordinate remains the same: 3
- y-coordinate changes sign: -2 becomes 2
- Reflected point: (3, 2)

3. **Reflecting the second point (-5, 4)**:
- Original point: (-5, 4)
- Applying the reflection rule:
- x-coordinate remains the same: -5
- y-coordinate changes sign: 4 becomes -4
- Reflected point: (-5, -4)

4. **Reflecting the third point (0, 0)**:
- Original point: (0, 0)
- Applying the reflection rule:
- x-coordinate remains the same: 0
- y-coordinate changes sign: 0 remains 0
- Reflected point: (0, 0)

### Final Reflected Points:
- (3, -2) reflects to (3, 2)
- (-5, 4) reflects to (-5, -4)
- (0, 0) reflects to (0, 0)

### Summary of Reflected Points:
1. (3, -2) → (3, 2)
2. (-5, 4) → (-5, -4)
3. (0, 0) → (0, 0)

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