Question

The transformation due to the reflection of $(x,y)$ through the

origin is described by the matrix

• A. $\begin{bmatrix} 0 & 0 \\ 0 & 1 \end{bmatrix}$
• B. $\begin{bmatrix}
  • 1 & 0 \ 0 & - 1 \end{bmatrix}$
• C. $\begin{bmatrix} 0 & - 1 \
  • 1 & 0 \end{bmatrix}$
• D. $\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$

Answer 1

Answer: (B)

$\begin{bmatrix}

• 1 & 0 \ 0 & - 1 \end{bmatrix}$

Answer 2

If $\left( x^{'},y^{'} \right)$ is the new position

$x ^ { \prime } = ( - 1 ) x + 0 . y$ $y^{'} = 0.x + ( - 1)yd$

$\therefore$ $\begin{bmatrix} x^{'} \ y^{'} \end{bmatrix} = \begin{bmatrix}

• 1 & 0 \ 0 & - 1 \end{bmatrix}\begin{bmatrix} x \ y \end{bmatrix}$

Transformation matrix is $\begin{bmatrix}

• 1 & 0 \ 0 & - 1 \end{bmatrix}$