To translate the vertices of triangle ABC by \( T_{1,6} \), we need to add \( 1 \) to the x-coordinates and \( 6 \) to the y-coordinates of each vertex.
Given the vertices:
- \( A(4, -2) \)
- \( B(-5, -1) \)
- \( C(5, 2) \)
We perform the translation as follows:
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For vertex \( A \): \[ A' = (4 + 1, -2 + 6) = (5, 4) \]
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For vertex \( B \): \[ B' = (-5 + 1, -1 + 6) = (-4, 5) \]
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For vertex \( C \): \[ C' = (5 + 1, 2 + 6) = (6, 8) \]
So, the vertices of triangle \( A'B'C' \) after the translation \( T_{1,6} \) are:
- \( A' = (5, 4) \)
- \( B' = (-4, 5) \)
- \( C' = (6, 8) \)
Thus, we write: The vertices of triangle \( \triangle A'B'C' \) are \( A' (5, 4) \), \( B' (-4, 5) \), and \( C' (6, 8) \).