To determine what kind of transformation has been applied to triangle ΔABC, we must analyze the coordinates of the points before and after the transformation.
Given the original points:
- A(-5, 4)
- B(-2, 2)
- C(5, -1)
And the transformed points:
- A'(7, 1)
- B'(4, -1)
- C'(3, 2)
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Translation: We first check if the points can be related through a translation. If we compare the coordinates directly, we do not find a consistent shift pattern that can be applied to all points.
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Rotation: We must determine if the original triangle can be rotated around a specific point to match the coordinates of the transformed triangle.
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Reflection: A reflection would require that the distance from the reflection line to corresponding points is equal. Thus, we must check if the new points lie symmetrically with respect to a line.
By inspecting the points closely:
- A to A' appears to move in a manner that suggests neither simply reflecting nor rotating around the origin.
- Analyzing the coordinates individually for rotation reveals inconsistencies that would not support a clean 90-degree or 180-degree configuration.
Since the points A, B, and C do not translate uniformly nor do they align to suggest a direct rotational movement, the transformation appears to involve a reflection across a line or axis.
Ultimately, without specific calculations, the kind of transformation done to ΔABC that fits the evidence presented leans towards a reflection.
Thus, the correct response is:
a reflection.