Answer
$\begin{bmatrix} 0&1&1\\-2&-2&-4\end{bmatrix}$
Work Step by Step
The matrix of the initial triangle's coordinates is:
$B=\begin{bmatrix}0&2&2\\0&0&-4\end{bmatrix}$
In order to half the perimeter of the triangle 2, we must divide each coordinate by 2.
In order to move the reduced triangle 2 units down, we must subtract 2 from each $y$-coordinate.
The translation matrix is:
$T=\begin{bmatrix} 0&0&0\\-2&-2&-2\end{bmatrix}$
Determine the new coordinates:
$\dfrac{1}{2}B+T=\dfrac{1}{2}\begin{bmatrix}0&2&2\\0&0&-4\end{bmatrix}+\begin{bmatrix} 0&0&0\\-2&-2&-2\end{bmatrix}$
$=\begin{bmatrix} 0&1&1\\0&0&-2\end{bmatrix}\begin{bmatrix} 0&0&0\\-2&-2&-2\end{bmatrix}$
$=\begin{bmatrix} 0+0&1+0&1+0\\0-2&0-2&-2-2\end{bmatrix}$
$=\begin{bmatrix} 0&1&1\\-2&-2&-4\end{bmatrix}$
