Solve Geometrical Transformations

Introduction

                                         Definition: Geometrical transformation is defined as , in an algebraic expression variables are changed by the geometrical transformation in which algebraic expression value is an another group of variables .In geometrical transformation, one space is mapping into another space or mapping itself. The geometrical transformation classified into may types which are discussed as follow:

 

Solving geometrical transformation methods:

 

1. Glide  or Reflection method.

2. Dilation method

3. Isometry method.

4. Slide or Translation method

5.Turn or Rotation method

6. Flip or Reflection method

1. Glide or Reflections methods:

Glide reflection method is composition of a translation method and reflection method.

2. Dilation method:

Dilation method, has a scale factor and a center, in this method the original image is smaller than enlargement – image and larger than the reduction –image.

3.  Isometry method:

Isometry method, an image and its original figure are in same shape and size (congruent).

 

4. Slide (or) Translation method:

                      Translation is which is used to replace the points same distance and in the same direction.

5. Turn (or) Rotations method:

   All points are in y degree, when an image is turned (or) rotated on that point.

6: Flip (or) Reflections method:

The same object will appear when we fold the object line. It is known as isometry.

 

 

solved examples of geometrical transformation:

 

Example1:

Under the translation to solve the image of point (4,-6) that shifts (a,b) to (a-2,b-4) is.....

Solution:

 (a,b) = (4, -6)

(a-2,b-4)=?

Here, a = 4 ;  b = -6.

(a-2,b-4) = (4-2,-4-6)

=  (2,10)

Answer is: (2,10).

Example 2:

  To solve the translation, if the  translation maps (a,b) (a+2,b+3) what are the coordinates of C (-3,5) after this translation?

Solution:

(a,b)= C(-3,4)

(a+2,b+3) = (-3+2,4+3)

= (-1,7)

The  solved coordinates of B (-3,5) after this translation is (-1,7).

Example 3:

To solve the image of point (2,-3) under the translation that shifts (a,b) to (a-1,b-3) is.....

Solution:

 (a,b) = (2, -3)

(a-12,b-3)=?

Here, a = 2 ;  b = -3.

(a-1,b-3) = (2-2,-3-6)

=  (0,-9)

The solved points are (0,-9)

Example 4:

To solve the image of point (3,-5) under the translation that shifts (a,b) to (a-1,b-3) is.....

Solution:

 (a,b) = (3, -5)

(a-12,b-3)=?

Here, a = 3 ;  b = -5.

(a-1,b-3) = (3-1,-3-5)

=  (2,-8)

Answer is: (2,-8).