Determine the effect of the following transformations
a) Rotation through pi/2, followed by projection on the Y axis, followed by reflection in the lines y=x.
b) Projection on the X axis followed by reflection in the line y=x.
Determine the effect of the following transformations
a) Rotation through pi/2, followed by projection on the Y axis, followed by reflection in the lines y=x.
b) Projection on the X axis followed by reflection in the line y=x.
It is easy to find the matrix of the rotation $\displaystyle R$ and the reflection $\displaystyle S$ :
$\displaystyle R \equiv \begin{bmatrix}{0}&{-1}\\{1}&{\;\;0}\end{bmatrix},\quad S \equiv \begin{bmatrix}{0}&{1}\\{1}&{0}\end{bmatrix}$
So,
$\displaystyle S\circ R\equiv \begin{bmatrix}{1}&{\;\;0}\\{0}&{-1}\end{bmatrix}$
that is, $\displaystyle S\circ R$ is the reflection in the $\displaystyle x$ axis.
Try b) .
Fernando Revilla