State the co-ordinates of the following points under reflection in the line x = 0 :
(i) (-6, 4) (ii) (0,5) (iii) (3, -4)

Answer

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

### Step 1: Identify the points
The points given are:
1. \( (-6, 4) \)
2. \( (0, 5) \)
3. \( (3, -4) \)

### Step 2: Reflect each point across the y-axis
When reflecting a point \( (x, y) \) across the y-axis, the x-coordinate changes its sign while the y-coordinate remains the same. The new coordinates will be \( (-x, y) \).

#### (i) Reflecting the point \( (-6, 4) \)
- Original point: \( (-6, 4) \)
- New coordinates after reflection: \( (6, 4) \)

#### (ii) Reflecting the point \( (0, 5) \)
- Original point: \( (0, 5) \)
- New coordinates after reflection: \( (0, 5) \) (the x-coordinate remains 0)

#### (iii) Reflecting the point \( (3, -4) \)
- Original point: \( (3, -4) \)
- New coordinates after reflection: \( (-3, -4) \)

### Step 3: State the final coordinates
The coordinates of the points after reflection in the line \( x = 0 \) are:
1. \( (6, 4) \)
2. \( (0, 5) \)
3. \( (-3, -4) \)

### Summary of Reflected Points:
- For \( (-6, 4) \) → \( (6, 4) \)
- For \( (0, 5) \) → \( (0, 5) \)
- For \( (3, -4) \) → \( (-3, -4) \)

---