Geometrical Transformations
Category : JEE Main & Advanced
(1) Reflexion in the x-axis: If \[P'\,\,(x',y')\]is the reflexion of the point \[P(x,y)\]on the x-axis, then the matrix \[\left[ \begin{matrix} 1 & 0 \\ 0 & -1 \\\end{matrix} \right]\] describes the reflexion of a point \[P(x,y)\]in the x-axis.
(2) Reflexion in the y-axis
Here the matrix is \[\left[ \begin{matrix} -1 & 0 \\ 0 & 1 \\\end{matrix} \right]\]
(3) Reflexion through the origin
Here the matrix is \[\left[ \begin{matrix} -1 & 0 \\ 0 & -1 \\ \end{matrix} \right]\]
(4) Reflexion in the line \[\mathbf{y=x}\]
Here the matrix is \[\left[ \begin{matrix} 0 & 1 \\ 1 & 0 \\ \end{matrix} \right]\]
(5) Reflexion in the line \[\mathbf{y=}-\mathbf{x}\]
Here the matrix is \[\left[ \begin{matrix} \,\,0 & -1 \\ -1 & \,\,0 \\ \end{matrix} \right]\]
(6) Reflexion in \[y=x\,\mathbf{tan\theta }\]
Here matrix is \[\left[ \begin{matrix} \cos 2\theta & \sin 2\theta \\ \sin 2\theta & -\cos 2\theta \\ \end{matrix} \right]\]
(7) Rotation through an angle \[\mathbf{\theta }\]
Here matrix is \[\left[ \begin{matrix} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \\ \end{matrix} \right]\]
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