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 $P$ through origin is

• 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. $\left(\begin{array}{cc}-1& 0\\ 0& 1\end{array}\right)$

Answer 1

The correct option is C $\left(\begin{array}{cc}-1& 0\\ 0& -1\end{array}\right)$

$P^{\prime }\left(x_1{y}_1\right)$ be the image of $P(x,y)$ through origin.

$\therefore x_1=-x=-1x+0y$ 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 through origin is given by the matrix

$\left(\begin{array}{cc}-1& 0\\ 0& -1\end{array}\right)$