The point A(-3, 2) is reflected in the x-axis to the point A'. Point A' is then reflected in the origin to point A".
Write down a single transformation that maps A onto A".

Answer

To solve the problem step by step, we will reflect the point A(-3, 2) in the x-axis and then reflect the resulting point in the origin to find the final point A". Finally, we will determine a single transformation that maps A onto A".

### Step 1: Reflect point A in the x-axis
- The coordinates of point A are (-3, 2).
- When a point (x, y) is reflected in the x-axis, the y-coordinate changes sign while the x-coordinate remains the same.
- Therefore, the reflection of A(-3, 2) in the x-axis gives us:
\[ A' = (-3, -2) \]

### Step 2: Reflect point A' in the origin
- Now we take point A' which is (-3, -2).
- When a point (x, y) is reflected in the origin, both the x and y coordinates change signs.
- Thus, the reflection of A'(-3, -2) in the origin gives us:
\[ A" = (3, 2) \]

### Step 3: Determine the single transformation that maps A onto A"
- We started with point A(-3, 2) and ended with point A"(3, 2).
- To find a single transformation that maps A to A", we can observe that the x-coordinate of A changes from -3 to 3 while the y-coordinate remains the same.
- This transformation can be described as a reflection in the y-axis.

### Final Answer
The single transformation that maps point A(-3, 2) onto point A"(3, 2) is a reflection in the y-axis.

---