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.

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- Feb 12th 2011, 05:57 PMseitDetermine the effect of the following transformations
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. - Feb 12th 2011, 11:33 PMFernandoRevilla
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