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 a single transformation that maps triangle ABC onto triangle A"B"C".

Answer

To find a single transformation that maps triangle ABC onto triangle A"B"C", we will follow these steps:

### Step 1: Reflect Triangle ABC in the y-axis
The coordinates of triangle ABC are:
- A(2, 6)
- B(-3, 5)
- C(4, 7)

When reflecting a point (x, y) in the y-axis, the new coordinates become (-x, y).

**Calculating the reflected points:**
- A' = (-2, 6) (from A(2, 6))
- B' = (3, 5) (from B(-3, 5))
- C' = (-4, 7) (from C(4, 7))

### Step 2: Reflect Triangle A'B'C' in the Origin
Now we will reflect the points A', B', and C' in the origin. When reflecting a point (x, y) in the origin, the new coordinates become (-x, -y).

**Calculating the reflected points:**
- A" = (2, -6) (from A'(-2, 6))
- B" = (-3, -5) (from B'(3, 5))
- C" = (4, -7) (from C'(-4, 7))

### Step 3: Determine the Single Transformation
The transformations we performed are:
1. Reflect in the y-axis.
2. Reflect in the origin.

To combine these transformations into a single transformation, we can analyze the final coordinates of A", B", and C".

The transformation can be described as:
- Reflecting first in the y-axis and then in the origin is equivalent to reflecting in the x-axis.

Thus, the single transformation that maps triangle ABC onto triangle A"B"C" is:
**Reflection in the x-axis.**

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