Question
In the transformation rotation at what degree measure image match with its pre image.
- 90°
- 180°
- 270°
- 360°
Hint:
Find the Angle of Rotation that gives exactly the same point on it's rotation.
The correct answer is: 360°
Given Data:
In the transformation rotation at what degree measure image match with its pre image.
>>>We were asked to find the Angle of Rotation that rotates to exactly to it's point.
>>>Hence, let the point in the space be (x, y) then it's rotation should be (x, y).
>>>Finely, The rotated coordinates are in the form:
(x', y') = 
>>>From the given data:
(x', y') = (x, y)
* By comparing the above Equation's we get:
x = (x cos
- y sin) and y = y cos + x sin
>>>By solving the above Equation's we get:
(x 
y) = (x y) cos - y2 sin
and (x y) = (x y) cos + x2sin
___________________________________
0 =(x2+y2)sin
-->sin=0
--> =360 degrees.
>>>Hence, the Angle of Rotation is 360 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
Related Questions to study
In the transformation rotation occurs with respect to
Rotation means the Circular movement of an object around one fixed point.
* Hence, it is called as a rigid transformation.
* Hence, we can say that the rotation meant that the rotation of an object about a fixed point.
In the transformation rotation occurs with respect to
Rotation means the Circular movement of an object around one fixed point.
* Hence, it is called as a rigid transformation.
* Hence, we can say that the rotation meant that the rotation of an object about a fixed point.
In which rotation movement does (x, y) 
(-x, -y)
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 which rotation movement does (x, y) (-x, -y)
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 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.
