Question

Let $P(x,y)$ be any given point and $P(x_1,y_1)$ be the image of $P(x,y)$ after reflection.

The matrix of reflection of point $P$ through the line $y=x$ is given by

• A. $\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$
• B. $\left[\begin{array}{cc}-1& 0\\ 0& -1\end{array}\right]$
• C. $\left[\begin{array}{cc}-1& 0\\ 0& 1\end{array}\right]$
• D. $\left[\begin{array}{cc}0& 1\\ 1& 0\end{array}\right]$

Answer 1

The correct option is D $\left[\begin{array}{cc}0& 1\\ 1& 0\end{array}\right]$

Reflection of matrix $P(x,y)$ through the line $y=mx$ making an angle $\theta$ with $x-$axis is

$\left[\begin{array}{cc}\cos 2\theta & \sin 2\theta \\ \sin 2\theta & -\cos 2\theta \end{array}\right]$
Given line is $y=x$ which makes an angle of ${45}^{\circ }$ with $x-$axis

Hence, the transformation matrix is $\left[\begin{array}{cc}0& 1\\ 1& 0\end{array}\right]$