Question

the vertices of a rectangle are given in the columns of the matrix ( r=\begin{bmatrix}0&0&3&3\\0&3&3&0end{bmatrix} ). if ( \begin{bmatrix}-1&0\\0&1end{bmatrix}\times r ) is found to perform a transformation, what are the coordinates of the transformed rectangle?
( (0,0),(0,-3),(-3,-3),(-3,0) )
( (0,0),(0,3),(3,3),(3,0) )
( (0,0),(0,3),(-3,-3),(-3,0) )
( (0,0),(0,3),(-3,3),(-3,0) )

Explanation:

Step1: Matrix multiplication

Multiply the matrices \(R=

$$\begin{bmatrix}0&0&3&3\\0&3&3&0\end{bmatrix}$$

\) and \(T =

$$\begin{bmatrix}-1&0\\0&1\end{bmatrix}$$

\).
For the first column of the product matrix:

$$
LATEXBLOCK2
$$

For the second column:

$$
LATEXBLOCK3
$$

For the third column:

$$
LATEXBLOCK4
$$

For the fourth column:

$$
LATEXBLOCK5
$$

Answer:

\((0,0),(0,3),(-3,3),(-3,0)\)