# JEE Main & Advanced Mathematics Determinants & Matrices Geometrical Transformations

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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