Which algebraic rule describes the 270° counter-clockwise rotation about the origin?

a) (x, y) → (-x, y)

b) (x, y) → (x, - y)

c) (x, y) → (y, - x)

d) (x, y) → (-y, x)

270 degree counter clockwise is the same as 90 degrees clockwise.

If you imagine the (x, y) axes rotating 90 clockwise, you will see that what x becomes y, and what was y becomes negative x (after the rotation).

So x-->y, and y-->-x

So the answer (c) is the correct one.