Attempt this question on graph paper.
Write down :
the single transformation that maps A' to A''.

Answer

To solve the problem of finding the single transformation that maps point A' to A'', we will follow these steps:

### Step-by-Step Solution:

1. **Assume Point A**:
Let's assume point A has coordinates (1, 2).

**Hint**: You can choose any point for A, but for this example, we will use (1, 2).

2. **Find A'**:
A' is the transformation of A about the x-axis. The transformation about the x-axis changes the y-coordinate to its negative while keeping the x-coordinate the same.
- So, A' = (x, -y) = (1, -2).

**Hint**: Remember that reflecting a point over the x-axis means changing the sign of the y-coordinate.

3. **Find A''**:
A'' is the transformation of A' about the origin. The transformation about the origin changes both the x and y coordinates to their negatives.
- Therefore, A'' = (-x, -y) = (-1, 2).

**Hint**: Reflecting a point over the origin means changing the signs of both coordinates.

4. **Determine the Transformation from A' to A''**:
Now we need to find the single transformation that maps A' to A''.
- A' = (1, -2) and A'' = (-1, 2).
- The transformation that maps (1, -2) to (-1, 2) is a reflection about the line y = x.

**Hint**: To find the transformation, think about how the coordinates change from A' to A''.

### Final Answer:
The single transformation that maps A' to A'' is a reflection about the line y = x.