Question

Predict what will happen to the coordinates of a point (x,y) as the point rotates counterclockwise (CCW) about the origin to produce point (x’,y’). Choose rotation angles of 90 degrees, 180 degrees, and 360 degrees. Express your answer in terms of x and y. Be sure to watch your signs.

Answer 1

Angle of Rotation (CCW) x′ y′

90° −y x

180° −x −y

270° y −x

360° x y

Answer 2

Explanation:

If a point (x, y) is rotated counterclockwise by the angles given in the table attached,

Rule for the rotation at an angle of 90° CCW about the origin,

(x, y) → (-y, x)

Rule for the rotation at an angle of 180° CCW about the origin,

(x, y) → (-x, -y)

Rule for the rotation at an angle of 270° CCW about the origin,

(x, y) → (y, -x)

Rule for the rotation at an angle of 360° CCW about the origin,

(x, y) → (x, y)

Angle of rotation x' y'

90° -y x

180° -x -y

270° y -x

360° x y