The triangle ABC, where A is (2, 6), B is (-3, 5) and C is (4, 7), is reflected in the y-axis to triangle A'B'C'. Triangle A'B'C' is then reflected in the origin to triangle A"B"C''.
Write down the co-ordinates of A", B" and C".

Answer

To solve the problem step by step, we will find the coordinates of the points A', B', and C' after the reflections as described.

### Step 1: Reflect triangle ABC in the y-axis to find triangle A'B'C'.

1. **Point A (2, 6)**: When reflecting over the y-axis, the x-coordinate changes sign. Therefore, A' = (-2, 6).
2. **Point B (-3, 5)**: Similarly, reflecting B over the y-axis gives B' = (3, 5).
3. **Point C (4, 7)**: Reflecting C over the y-axis results in C' = (-4, 7).

So, after the reflection in the y-axis, the coordinates are:
- A' = (-2, 6)
- B' = (3, 5)
- C' = (-4, 7)

### Step 2: Reflect triangle A'B'C' in the origin to find triangle A"B"C''.

1. **Point A' (-2, 6)**: When reflecting over the origin, both coordinates change sign. Thus, A" = (2, -6).
2. **Point B' (3, 5)**: Reflecting B' over the origin gives B" = (-3, -5).
3. **Point C' (-4, 7)**: Reflecting C' over the origin results in C" = (4, -7).

So, after the reflection in the origin, the coordinates are:
- A" = (2, -6)
- B" = (-3, -5)
- C" = (4, -7)

### Final Coordinates:
- A" = (2, -6)
- B" = (-3, -5)
- C" = (4, -7)