Question
The rule (x, y) → ( - y, - x) describes
- Reflection of point over the line y = x
- Reflection of point over the line y = - x
- Rotation of point 90° counter clockwise
- Rotation of point 90° clockwise
Hint:
A rotation is a transformation in a plane that turns every point of a preimage through a specified angle and direction about a fixed point.
The correct answer is: Reflection of point over the line y = - x
The rule (x, y) → ( - y, - x) describes reflection about the line y = x.
Hence, the correct option is A.
A point can be reflected about any of the two axes or about any line.
Related Questions to study
The rule (x, y) → (y, x) describes
A point can be reflected about any of the two axes or about any line.
The rule (x, y) → (y, x) describes
A point can be reflected about any of the two axes or about any line.
What is an isometric transformation?
A point can be reflected about any of the two axes or about any line.
What is an isometric transformation?
A point can be reflected about any of the two axes or about any line.
Which rule shows a translation 6 units right
A point can be reflected about any of the two axes or about any line.
Which rule shows a translation 6 units right
A point can be reflected about any of the two axes or about any line.
If a figure undergoes translation and then reflection then the image after transformation will be
A rotation is a transformation in a plane that turns every point of a preimage through a specified angle and direction about a fixed point.
If a figure undergoes translation and then reflection then the image after transformation will be
A rotation is a transformation in a plane that turns every point of a preimage through a specified angle and direction about a fixed point.
Which composite transformation is not rigid
In mathematics, a rigid transformation is a geometric transformation of a Euclidean space that preserves the Euclidean distance between every pair of points.
Which composite transformation is not rigid
In mathematics, a rigid transformation is a geometric transformation of a Euclidean space that preserves the Euclidean distance between every pair of points.
Which term is related to rotation
Hence, we can say that Rotation Concept is related to rotates.
Which term is related to rotation
Hence, we can say that Rotation Concept is related to rotates.
Which is not the property of the transformation rotation
Hence, we can say that the similarity is not a property of the transformation.
Which is not the property of the transformation rotation
Hence, we can say that the similarity is not a property of the transformation.
From the given transformation which pre image is not equal to image
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.
From the given transformation which pre image is not equal to image
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.
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.
