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A sequence of transformations maps AABCTO AABC. The sequence of transformations that maps ABC to ABC is a reflection across
followed by a translation
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The sequence of transformations that maps ΔABC to ΔA'B'C' is the reflection across the line y = x and a translation 10 units right and 4 units up, equivalent to T₍₁₀, ₄₎

Step-by-step explanation:

For a reflection across the line y = -x, we have, (x, y) → (y, x)

Therefore, the point of the preimage A(-6, 2) before the reflection, becomes the point A''(2, -6) after the reflection across the line y = -x

The translation from the point A''(2, -6) to the point A'(12, -2) is T(10, 4)

Given that rotation and translation transformations are rigid transformations, the transformations that maps point A to A' will also map points B and C to points B' and C'

Therefore, a sequence of transformation maps ΔABC to ΔA'B'C'. The sequence of transformations that maps ΔABC to ΔA'B'C' is the reflection across the line y = x and a translation 10 units right and 4 units up, which is T₍₁₀, ₄₎