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The question asks which transformation best supports the conclusion that Figure \( M \) is congruent to Figure \( M' \). We are provided with a coordinate grid showing the two figures. Let's analyze the options and the transformation that occurred between \( M \) and \( M' \).

1. **Translation (Option 1 and 3)**:
   - Translation means shifting the figure by a certain amount along the x-axis and/or y-axis. Based on the visual, it doesn't seem like a simple translation, as Figure \( M' \) appears rotated.

2. **Reflection (Option 2)**:
   - A reflection across the x-axis would flip the figure, but Figure \( M' \) is not a mirror image of Figure \( M \).

3. **Rotation (Option 4)**:
   - Rotation preserves the shape and size of the figure, but changes its orientation. By observing Figure \( M \) and \( M' \), it looks like Figure \( M \) has been rotated by 180° around the origin. The orientation of Figure \( M' \) is inverted compared to Figure \( M \), which is consistent with a 180° rotation.

Therefore, the best answer is **Option 4**: *Figure \( M \) was rotated 180° about the origin to produce Figure \( M' \)*.

Would you like more details about the transformations?

Here are some related questions:
1. What is the difference between reflection and rotation in transformations?
2. How can we determine if two figures are congruent after a transformation?
3. What are the effects of rotating a figure 180° on a coordinate plane?
4. Can a figure be congruent after a reflection?
5. What is the mathematical definition of translation?

**Tip**: When a figure is rotated 180° around the origin, each point \( (x, y) \) of the figure maps to \( (-x, -y) \).

Which statement best supports the conclusion that Figure M is congruent to Figure M'?

Explore how different transformations affect the congruence of figures on a coordinate grid. Learn which transformations, including rotation, reflection, and translation, maintain congruence and why a 180° rotation about the origin makes Figure M congruent to Figure M'. Suitable for Grades 8-10 students.

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