Question

HELP 5 STAR + THANKS What series of transformations from △ABC to ​ △DEF ​ shows that △ABC≅△DEF ? a reflection across the y-axis followed by a translation of 1 unit right and 2 units up a clockwise rotation of 90° about the origin followed by a translation of 4 units right and 4 units up a reflection across the x-axis followed by a translation of 1 unit right and 1 unit down a reflection across the line y = x followed by a positive rotation of 270° about the center

Answer 1

In the given triangle, the verteces are A(-4, 1), B(-6, 5), C(-1, 2).
A refrection across the x-axis will result in A'(-4, -1), B'(-6, -5), C'(-1, -2)
A translation of 1 unit to the right will result in A"(-3, -1), B"(-5, -5), C"(0, -2)
A translation of 1 unit down will result in A"'(-3, -2), B"'(-5, -6), C"'(0, -3) which corresponds to points DEF.
Therefore, the series of transformation required to transform ABC to DEF are a reflection across the x-axis followed by a translation of 1 unit right and 1 unit down.