Question
In which rotation movement does (x, y) 
(-x, -y)
- CCW 90° and CW 270°
- CW 90°
- CW180° and CCW180°
- CCW 270°
Hint:
TO find the Angle of Rotation, we need compare both the point and it's rotation point.
The correct answer is: CW180° and CCW180°
Given Data:
In which rotation movement does (x, y) (-x, -y)
***we were asked to find the Angle of Rotation of a point (x, y) to rotate it to (-x, -y).
>>>The rotated coordinates are:
(x', y') = (x cos
- y sin , y cos + x sin)
>>>From the data given (x', y') = (-x, -y)
* Hence, By comparing the above equation's we get:
-x = x cos - y sin and -y = y cos + x sin. Then
* By solving the above equation's we get:
(y 
- x) = (y x ) cos - y2 sin
(-y x) = (y x ) cos + x2sin
___________________________________
0 = 0 + (x2+y2)sin
sin=0
= 180 degrees or -180 degrees.
***Hence, the Angle of Rotation to rotate the point (x, y) to (-x, -y) is counter clockwise 180 degrees and clockwise 180 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).
Related Questions to study
In which rotation movement does (x, y) (-y, x)
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) = y2 cos + (x y)sin
________________________________
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 which rotation movement does (x, y) (-y, x)
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) = y2 cos + (x y)sin
________________________________
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 rotation of clockwise movement maps (x , y) 
(y,-x)
Given Data:
The point (x, y) is transformed to (x , y) (y,-x) in clockwise direction.
>>> we were asked to find the Angle of Rotation.
>>>The coordinates of a point (x, y) after rotation through 90 degrees in clockwise direction are:
(x', y') = (x cos - y sin , y cos + x sin)
>>>we were given that (x', y') = (y, -x)
>>> (y, -x) = (x cos - y sin , y cos + x sin)
Hence, y = x cos - y sin and -x = y cos + x sin
By solving the above equation's we get:
(x y) = x2cos - (x y) sin
and (y -x) = y2cos + (x y) sin
__________________________________
0 = (x2+y2)cos
*This implies cos=0, then: = 90 degrees.
>>>Therefore, the angle of rotation is 90 degrees.
In rotation of clockwise movement maps (x , y) (y,-x)
Given Data:
The point (x, y) is transformed to (x , y) (y,-x) in clockwise direction.
>>> we were asked to find the Angle of Rotation.
>>>The coordinates of a point (x, y) after rotation through 90 degrees in clockwise direction are:
(x', y') = (x cos - y sin , y cos + x sin)
>>>we were given that (x', y') = (y, -x)
>>> (y, -x) = (x cos - y sin , y cos + x sin)
Hence, y = x cos - y sin and -x = y cos + x sin
By solving the above equation's we get:
(x y) = x2cos - (x y) sin
and (y -x) = y2cos + (x y) sin
__________________________________
0 = (x2+y2)cos
*This implies cos=0, then: = 90 degrees.
>>>Therefore, the angle of rotation is 90 degrees.
is 54o, find the measure of d.
