In which rotation movement does (x, y)      (-y, x)

The correct answer is: CCW 90° and CW 270°

Given Data:
In which rotation movement does (x, y)      (-y, x)
>>>We were asked to find the angle of rotation of a point to rotate a point from (x, y) to (-y, x).
*** Rotated coordinates are:
(x', y') =  (x cos - y sin , y cos + x sin)
>>Here, the rotated points are :
(x', y') = (-y, x).
* Hence, By comparing the above equation's we get:
             -y =  x cos - y sin ; and x = y cos + x sin
Hence, By solving the above equation's we get:

            (x  -y) = x²cos - (x  y)sin
and      (y  x) = y²cos + (x  y)sin
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0 = ( x² + y²)cos
* Hence, cos =0 leads to 90 degrees or -270 degrees.
>>>>Therefore, the Angle of Rotation is counter clockwise 90 degrees and clockwise 270 degrees.

* In Mathematics, rotation means the Circular movement of an object around one fixed point.

* In rotation, the image after transformation remains constant.

* Hence, it is called as a rigid transformation.

* No Change in shape and size.

* The Shape rotates counter- clockwise when the degrees is positive and rotates clockwise when degrees is negative.

*The Rotation of a point (x, y) about origin and through angle alpha, then:
New coordinates of a point (x, y) after it's rotation becomes (x cos - y sin , y cos + x sin).