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 $(-x, -y)$.