https://file.aiquickdraw.com/mathbot/file/1727394024529s416volm.jpg

The problem asks which transformation transforms Figure \( M \) into Figure \( N \).

Looking at the graph, the shapes \( M \) and \( N \) seem to be congruent, indicating that a rigid motion (a transformation that preserves distance and angles) was used.

### Step-by-step analysis:
1. **Reflection**: The shapes \( M \) and \( N \) appear to be mirror images across the \( y \)-axis. This indicates a reflection about the \( y \)-axis.

2. **Verifying Coordinates**: 
   - Figure \( M \) is on the negative side of the \( x \)-axis (to the left of the \( y \)-axis).
   - Figure \( N \) is on the positive side of the \( x \)-axis (to the right of the \( y \)-axis).
   - The relative position and orientation between the figures suggest a reflection across the \( y \)-axis.

Thus, the correct transformation is **reflection across the \( y \)-axis**.

Do you need more details or have any questions?

Here are five follow-up questions to deepen your understanding:
1. What is the general rule for reflecting a point across the \( y \)-axis?
2. How can you identify if a transformation is a reflection?
3. What are the other types of rigid motions, and how do they differ from reflection?
4. What properties of a shape are preserved under reflection?
5. Could you have performed a rotation or translation to achieve the same result in this case?

**Tip**: Always check both the position and orientation of figures when identifying transformations like reflections or rotations.

Figure N is the result of a transformation on Figure M. Which transformation would accomplish this?

Learn how to identify rigid transformations with this example problem. Figure N is the reflection of Figure M across the y-axis. Understand key concepts such as rigid motions and the reflection theorem. Suitable for students in Grades 7-9.

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