State the co-ordinates of the following points under reflection in the line y = 0,
(i) (-3, 0) (ii) (8, -5) (iii) (-1, -3)

Answer

To find the coordinates of the given points under reflection in the line \( y = 0 \) (the x-axis), we need to follow these steps:

### Step 1: Understand the Reflection Rule
When reflecting a point across the x-axis, the x-coordinate remains the same while the y-coordinate changes its sign.

### Step 2: Reflect the First Point (-3, 0)
- The coordinates of the first point are \((-3, 0)\).
- Since the y-coordinate is \(0\), reflecting this point across the x-axis will not change its position.
- Therefore, the reflected point is \((-3, 0)\).

### Step 3: Reflect the Second Point (8, -5)
- The coordinates of the second point are \((8, -5)\).
- The x-coordinate remains \(8\) and the y-coordinate changes from \(-5\) to \(5\).
- Therefore, the reflected point is \((8, 5)\).

### Step 4: Reflect the Third Point (-1, -3)
- The coordinates of the third point are \((-1, -3)\).
- The x-coordinate remains \(-1\) and the y-coordinate changes from \(-3\) to \(3\).
- Therefore, the reflected point is \((-1, 3)\).

### Summary of Reflected Points
1. The reflection of \((-3, 0)\) is \((-3, 0)\).
2. The reflection of \((8, -5)\) is \((8, 5)\).
3. The reflection of \((-1, -3)\) is \((-1, 3)\).

### Final Answer
- (i) \((-3, 0)\)
- (ii) \((8, 5)\)
- (iii) \((-1, 3)\)

---