To determine the type of transformation from triangle ABC to triangle A'B'C', we can analyze how each point transforms.
Given the points:
- A = (0, 5) → A' = (0, 2.5)
- B = (5, 7) → B' = (2.5, 3.5)
- C = (7, 0) → C' = (3.5, 0)
Let's first look at the change in position of each vertex:
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The point A = (0, 5) transforms to A' = (0, 2.5). This indicates a vertical movement downward by 2.5 units.
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The point B = (5, 7) transforms to B' = (2.5, 3.5). The transformation involves a horizontal shift of -2.5 units and a vertical shift of -3.5 units.
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The point C = (7, 0) transforms to C' = (3.5, 0). This indicates a horizontal movement of -3.5 units, but no vertical change.
Analysis of Transformation:
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A translation would keep the shape intact and only move the entire triangle without altering the lengths of its sides or angles. The different transformations for each point suggest an inconsistent change in the triangle's positions.
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A rigid transformation like a reflection or rotation would keep the lengths and angles the same, which does not appear to hold true here since the lengths of segments and the distances from the origin change.
Given the vertical and horizontal shifts of the points do not match up equally (they have different changes), this indicates that a rigid transformation cannot account for these changes uniformly.
Conclusion:
Based on the analysis, the answer is A. no rigid transformation can make this happen.