Questions: Error Analysis Emilia was asked to find the coordinates of (D2(triangle A B C)) for (A(2,4), B(0,5)), and (C(-2,1)). What is Emilia's error? [ A(2,4) rightarrow A'(4,6) B(0,5) rightarrow B'(2,7) C(-2,1) rightarrow C'(0,3) ]

Solution Steps

The original coordinates of the triangle vertices are given as:

• \( A(2, 4) \)
• \( B(0, 5) \)
• \( C(-2, 1) \)

The transformed coordinates are:

• \( A'(4, 6) \)
• \( B'(2, 7) \)
• \( C'(0, 3) \)

To find the transformation applied to each point, we calculate the differences between the transformed and original coordinates:

• For point \( A \): \[ A' - A = (4 - 2, 6 - 4) = (2, 2) \]
• For point \( B \): \[ B' - B = (2 - 0, 7 - 5) = (2, 2) \]
• For point \( C \): \[ C' - C = (0 - (-2), 3 - 1) = (2, 2) \]

The transformations for all three points yield the same result: \[ \text{Transformation} = (2, 2) \] This indicates that the same transformation was applied consistently across all points.

Emilia's error lies in the assumption that the transformation was different for each point. Instead, the transformation is uniform, indicating that each point was translated by the vector \( (2, 2) \). Thus, the correct transformation should have been applied uniformly rather than assuming individual transformations.

Final Answer