Chapter 14.7, Problem 30WE

a

To determine

To find how is translation S related to translation T.

Answer to Problem 30WE

Transformation S = Inverse of a transformation T

Explanation of Solution

Given information :

  ${\text{H}}_A\circ H_B$ = Translation S

  $H_B\circ H_A$ = Translation T

Such that $S\circ T=I$

  $S=T^{-1}$

Hence,

Transformation S = Inverse of a transformation T

b

To determine

To prove that $\left({\text{H}}_A\circ H_B\right)(H_B\circ H_A)=I$

Answer to Problem 30WE

  $\left({\text{H}}_A\circ H_B\right)(H_B\circ H_A)=I$ is verified

Explanation of Solution

Given information :

  ${\text{H}}_A\circ H_B$ = Translation S

  $H_B\circ H_A$ = Translation T

  $\begin{array}{l}L.H.S.=\left({\text{H}}_A\circ H_B\right)(H_B\circ H_A)\\ =\left({\text{H}}_A\circ H_B\right){\left({\text{H}}_A\circ H_B\right)}^{-1}\\ =I\\ =R.H.S\end{array}$

Hence,

  $\left({\text{H}}_A\circ H_B\right)(H_B\circ H_A)=I$ is verified