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 $P$ in $y$-axis is

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

Answer 1

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

The reflection matrix of $P(x,y)$ in $y-$axis is the point $P^{\prime }\left(x_1{y}_1\right)$

$\therefore x_1=-x=-1x+0y$

and $y_1=y=0x+1y$

$\therefore \left[\begin{array}{c}{x}_1\\ y_1\end{array}\right]=\left[\begin{array}{cc}-1& 0\\ 0& 1\end{array}\right]\left[\begin{array}{c}x\\ y\end{array}\right]$

$\therefore$ Matrix of reflection of $P(x,1^{\prime })$ in $y-$axis is given by the matrix $\left[\begin{array}{cc}-1& 0\\ 0& 1\end{array}\right]$

$\therefore$ Choice (b) is correct.