Question

Given △PQR with vertices P(−1,2)​, Q(2,4)​, and R(−4,5)​, write the translation equivalent to the composition of transformations. The equation of line t is y=8. rt◦rx-axis

Answer 1

The translation equivalent to the composition of transformations is P''(-1,6), Q''(2,4), and R''(-4,3).

Step-by-step explanation:

The composition of transformations is the combination of two or more transformations. We are given two transformations: rt and rx-axis. A translation is represented by rt and the equation of line t is y=8. A reflection over the x-axis is represented by rx-axis. To find the translation equivalent to the composition of transformations, we first apply the reflection rx-axis to triangle PQR. The image of triangle PQR after the reflection is P'(-1,-2), Q'(2,-4), and R'(-4,-5). Then, we apply the translation rt, which moves each point of the reflected triangle 8 units up. The translation equivalent to the composition of transformations is P''(-1,6), Q''(2,4), and R''(-4,3).

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