Question

What set of reflections and rotations would carry rectangle ABCD onto itself?

Rectangle formed by ordered pairs A at negative 4, 1, B at negative 4, 2, C at negative 1, 2, D at negative 1, 1.

Answer 1

Locate the two lines that bisect the ends or sides.
Those are the axes of reflection

naturally, rotating halfway around the center also works

So just write those operations in your notation