Question

the vertices of a triangle are given in the columns of the matrix $t = \

$$\begin{bmatrix} 0 & 4 & 0 \\\\ 0 & 0 & 5 \\end{bmatrix}$$

$. if $\

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

\times t$ is found to perform a transformation, what are the coordinates of the transformed triangle?
\bigcirc \\ (0, 0), (-4, 0), (0, -5)
\bigcirc \\ (0, 0), (-4, 0), (0, 5)
\bigcirc \\ (0, 0), (4, 0), (0, -5)
\bigcirc \\ (0, 0), (4, 0), (0, 5)

Explanation:

Step1: Matrix multiplication

Let \(A=

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

\) and \(T =

$$\begin{bmatrix}0&4&0\\0&0&5\end{bmatrix}$$

\).
The product \(AT\) is calculated as follows:

$$
LATEXBLOCK2
$$

The columns of the matrix \(AT\) give the coordinates of the vertices of the transformed triangle.

Answer:

\((0,0),(-4,0),(0, - 5)\) (First option)