Question

What transformation is represented by the rule
(x,  y)→(−y,  x)

Answer 1

it is going from quadrant 1 to quadrant 4.

it is reflected right?

sorry it has been a while since I have done this but I hope it helps :)

Answer 2

x and y are switched and y times -1 so

reflection across the x=y line (identiy line)
and since the x place it times -1, that is a reflection across y axis

so reflection across x=y line and y axis