What series of transformations map △abc onto △def to prove that △abc≅△def ?

a reflection across y-axis then translation of 1 unit right and 2 units up.

a clockwise rotation of 180° about the origin then a translation of 1 unit right and 3 units up

a reflection across y-axis then translation of 1 unit right and 1 unit down

a reflection across y = x then a positive rotation of 270° about the origin

The answer is a clockwise rotation of 180° about the origin then a translation of 1 unit right and 3 units up

In the given diagram A(5, 2), B(5, 6), C(2, 2);
a clockwise rotation of 180 degrees about the origin takes the triangle to the points A'(-5, -2), B'(-5, -6), C'(-2, -2).
A translation of 1 unit to the right results in A"(-4, -2), B"(-4, -6), C"(-1, -2).
A translation of 3 units up results in A"'(-4, 1), B"'(-4, -3), C"'(-1, 1) which corresponds to points DEF.
Therefore, the series of transformations on ABC to result in DEF are a clockwise rotation of 180° about the origin then a translation of 1 unit right and 3 units up