The  rule (x , y) → ( - x ,   - y) describe

A point can be reflected about any of the two axes or about any line.

A point can be reflected about any of the two axes or about any line.

A point can be reflected about any of the two axes or about any line.

A point can be reflected about any of the two axes or about any line.

A point can be reflected about any of the two axes or about any line.

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.

In mathematics, a rigid transformation is a geometric transformation of a Euclidean space that preserves the Euclidean distance between every pair of points.

Hence, we can say that Rotation Concept is related to rotates.

Hence, we can say that the similarity is not a property of the transformation.

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.

* 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.

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.

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
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0 =(x²+y²)sin
-->sin=0
-->    =360 degrees.
>>>Hence, the Angle of Rotation is 360 degrees.

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.

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.