Transformation

After completion of this chapter, students will be able to:

  • know about the combination of transformations and transformation using matrix.
  • solve the problems of combination of transformations.
  • solve the problems of transformation using matrix.

Notes

Combination of Transformations

If the point P is transformed by the transformation R1 to the point 'p' is again transformed by the transformation R2 to the point P", then the transformation which maps the point P to p" is said to be the combined transformation of R1 and R2. It is denoted by R2 .R1. The transformation R2.R. is also written as R2. R1

Transformation Using Matrix

Matrix is the powerful mathematical tool. It simplifies the mathematical problems in short cut and easy way. Most of the elementary geometrical transformation can be performed by the use of matrices.

Transformation by 2 x 1 matrix

Transformation using 2 x 2 matrices

 

Reflection using 2 x 2 Matrices

(a) Reflection in X-axis

(b) Reflection in y-axis

(c) Reflection in the line y = x

Rotation using 2 x 2 Matrices

(a) Positive Quarter turn about the origin

 (b) Negative Quarter turn about the origin

(c) Half turn about origin

 

Enlargement using 2 x 2 Matrices

(a) Enlargement with centre (0, 0) and scale factor k.

(b) Enlargement with centre (a,b) and scale factor k.