Question

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)

Answer 1

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.

Answer 2

option C

Explanation:

the correct answer is option C

when a point (x, y ) means point lies in the first quadrant is rotated counter-clockwise to 270° means now the point will be in the fourth quadrant.

hence, in algebraic notation we interchange x by negative x

and y remains the same and their value interchanges so,

the best-suited answer will be (x, y) → (y, -x)

hence, the answer will be option C