Question
From the given transformation which pre image is not equal to image
- Reflection
- Rotation
- Translation
- Dilation
Hint:
General Synopsis of Transformations.
The correct answer is: Dilation
Transformation is a mechanism that transform an object into different structures.
In General, there are 4 types of transformations. They are;
1. Reflection
2. Rotation
3 Translation
4. Dilation.
Except Dilation, all the transformation techniques are termed as rigid transformations since, they provide same structure as the object.
* In General Transformation is of 4 types. They are Reflection, Rotation, Dilation, Translation.
* Except the Dilation all the transformations are Rigid Transformations.
* 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
From the given transformation which is not a rigid transformation
* Transformation is the mechanism that changes one image to other by performing the below techniques.
* Reflection, Rotation, Dilation, Translation.
* Since, In Reflection, Rotation, Dilation the size and shape of the object remains constant. They were called as Rigid Transformation.
* In Dilation, the object's structure got changed and hence, it is termed as a non- rigid Transformation.
From the given transformation which is not a rigid transformation
* Transformation is the mechanism that changes one image to other by performing the below techniques.
* Reflection, Rotation, Dilation, Translation.
* Since, In Reflection, Rotation, Dilation the size and shape of the object remains constant. They were called as Rigid Transformation.
* In Dilation, the object's structure got changed and hence, it is termed as a non- rigid Transformation.
Pick the odd one out
Hence, we can say that only one option that Rotation is a transformation which slides across the plane is wrong because the rotation transition always slide across a point.
Pick the odd one out
Hence, we can say that only one option that Rotation is a transformation which slides across the plane is wrong because the rotation transition always slide across a point.
In the transformation rotation at what degree measure image match with its pre image.
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 the transformation rotation at what degree measure image match with its pre image.
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 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.
