Mathematics
Grade-8
Easy

Question

Pick the odd one out

  1. Rotation is a isometric transformation
  2. Rotation is a rigid transformation
  3. Rotation is a transformation which occurs with respect to fixed point
  4. Rotation is a transformation which slides across the plane

hintHint:

General synopsis of Rotation concept.

The correct answer is: Rotation is a transformation which slides across the plane


    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 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 cosalpha - y sinalpha , y cosalpha + x sinalpha)

    Related Questions to study

    Grade-8
    Mathematics

    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') =  left parenthesis x space cos alpha space minus space y space sin alpha space comma space y space cos alpha space plus space x space sin alpha right parenthesis
    >>>From the given data:
    (x', y') = (x, y)
    * By comparing the above Equation's we get:
    x = (x cosalpha - y sinalpha) and y = y cosalpha + x sinalpha
    >>>By solving the above Equation's we get:
              (x cross times y) =  (x cross times y) cosalpha - y2 sinalpha
    and    (x cross times y) =   (x cross times y) cosalpha + x2sinalpha
    ___________________________________
    0 =(x2+y2)sinalpha
    -->sinalpha=0
    -->    alpha=360 degrees.
    >>>Hence, the Angle of Rotation is 360 degrees.

    In the transformation rotation at what degree measure image match with its pre image.

    MathematicsGrade-8

    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') =  left parenthesis x space cos alpha space minus space y space sin alpha space comma space y space cos alpha space plus space x space sin alpha right parenthesis
    >>>From the given data:
    (x', y') = (x, y)
    * By comparing the above Equation's we get:
    x = (x cosalpha - y sinalpha) and y = y cosalpha + x sinalpha
    >>>By solving the above Equation's we get:
              (x cross times y) =  (x cross times y) cosalpha - y2 sinalpha
    and    (x cross times y) =   (x cross times y) cosalpha + x2sinalpha
    ___________________________________
    0 =(x2+y2)sinalpha
    -->sinalpha=0
    -->    alpha=360 degrees.
    >>>Hence, the Angle of Rotation is 360 degrees.

    Grade-8
    Mathematics

    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

    MathematicsGrade-8

    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.

    Grade-8
    Mathematics

    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 cosalpha - y sinalpha , y cosalpha + x sinalpha)
    >>>From the data given  (x', y') = (-x, -y)
    * Hence, By comparing the above equation's we get:
                   -x = x cosalpha - y sinalpha and  -y = y cosalpha + x sinalpha. Then
    * By solving the above equation's we get:
                  (y cross times- x) = (y cross times x ) cosalpha - y2 sinalpha
                  (-y cross times x) = (y cross times x ) cosalpha + x2sinalpha
                ___________________________________
                           0   = 0 + (x2+y2)sinalpha

    sinalpha=0
    alpha = 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)

    MathematicsGrade-8

    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 cosalpha - y sinalpha , y cosalpha + x sinalpha)
    >>>From the data given  (x', y') = (-x, -y)
    * Hence, By comparing the above equation's we get:
                   -x = x cosalpha - y sinalpha and  -y = y cosalpha + x sinalpha. Then
    * By solving the above equation's we get:
                  (y cross times- x) = (y cross times x ) cosalpha - y2 sinalpha
                  (-y cross times x) = (y cross times x ) cosalpha + x2sinalpha
                ___________________________________
                           0   = 0 + (x2+y2)sinalpha

    sinalpha=0
    alpha = 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.

    parallel
    Grade-8
    Mathematics

    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 cosalpha - y sinalpha , y cosalpha + x sinalpha)
    >>Here, the rotated points are :
                  (x', y') = (-y, x).
    * Hence, By comparing the above equation's we get:
                 -y =  x cosalpha - y sinalpha ; and x = y cosalpha + x sinalpha

    Hence, By solving the above equation's we get:

                (x cross times -y) = x2cosalpha - (x cross times y)sinalpha

    and      (y cross times x) = y2 cosalpha + (x cross times y)sinalpha
              ________________________________
                          0 = ( x2 + y2)cosalpha 

    * Hence, cosalpha =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)

    MathematicsGrade-8

    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 cosalpha - y sinalpha , y cosalpha + x sinalpha)
    >>Here, the rotated points are :
                  (x', y') = (-y, x).
    * Hence, By comparing the above equation's we get:
                 -y =  x cosalpha - y sinalpha ; and x = y cosalpha + x sinalpha

    Hence, By solving the above equation's we get:

                (x cross times -y) = x2cosalpha - (x cross times y)sinalpha

    and      (y cross times x) = y2 cosalpha + (x cross times y)sinalpha
              ________________________________
                          0 = ( x2 + y2)cosalpha 

    * Hence, cosalpha =0 leads to 90 degrees or -270 degrees.
    >>>>Therefore, the Angle of Rotation is counter clockwise 90 degrees and clockwise 270 degrees.

    Grade-8
    Mathematics

    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 cosalpha - y sinalpha , y cosalpha + x sinalpha)
    >>>we were given that (x', y') = (y, -x)
    >>> (y, -x) = (x cosalpha - y sinalpha , y cosalpha + x sinalpha)
        Hence, y = x cosalpha - y sinalpha and -x = y cosalpha + x sinalpha
    By solving the above equation's we get:
                  (x cross times y)  = x2cosalpha - (x cross times y) sinalpha
    and        (y cross times -x) = y2cosalpha + (x cross times y) sinalpha

    __________________________________
    0 = (x2+y2)cosalpha
    *This implies cosalpha=0, then:
    alpha = 90 degrees.
    >>>Therefore, the angle of rotation is 90 degrees.

    In rotation of clockwise movement maps (x , y) (y,-x)

    MathematicsGrade-8

    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 cosalpha - y sinalpha , y cosalpha + x sinalpha)
    >>>we were given that (x', y') = (y, -x)
    >>> (y, -x) = (x cosalpha - y sinalpha , y cosalpha + x sinalpha)
        Hence, y = x cosalpha - y sinalpha and -x = y cosalpha + x sinalpha
    By solving the above equation's we get:
                  (x cross times y)  = x2cosalpha - (x cross times y) sinalpha
    and        (y cross times -x) = y2cosalpha + (x cross times y) sinalpha

    __________________________________
    0 = (x2+y2)cosalpha
    *This implies cosalpha=0, then:
    alpha = 90 degrees.
    >>>Therefore, the angle of rotation is 90 degrees.

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