91Ó°ÊÓ

A translation of a figure is said to occur when a figure is moved from one location to other without having change in its size, shape or orientation.

The vertex matrix for the triangle $ABC$ is given by:$\left[\begin{array}{ccc}0& −3& −2\\ 2& −1& −4\end{array}\right]$

As the given triangle is translated 1 unit right and 3 units up therefore to translate the given figure, add $1$to each $x$-coordinate and add 3 to each $y$-coordinate.

Therefore the translation matrix has each column as $\left[\begin{array}{c}1\\ 3\end{array}\right]$.

Therefore, the translation matrix is given by:$\left[\begin{array}{ccc}1& 1& 1\\ 3& 3& 3\end{array}\right]$

The vertex matrix of the triangle $\mathrm{Δ}A\text{'}B\text{'}C\text{'}$can be find out by adding the vertex matrix for the triangle $ABC$with the translation matrix.

Therefore, the vertex matrix of the triangle $\mathrm{Δ}A\text{'}B\text{'}C\text{'}$is given by:

$\begin{array}{c}\text{vertexmatrixforΔ´¡'B'C}\text{'}=\left[\begin{array}{ccc}0& −3& −2\\ 2& −1& −4\end{array}\right]+\left[\begin{array}{ccc}1& 1& 1\\ 3& 3& 3\end{array}\right]\\ =\left[\begin{array}{ccc}0+1& −3+1& −2+1\\ 2+3& −1+3& −4+3\end{array}\right]\\ =\left[\begin{array}{ccc}1& −2& −1\\ 5& 2& −1\end{array}\right]\end{array}$

Therefore, the coordinates of the triangles $\mathrm{Δ}A\text{'}B\text{'}C\text{'}$ are: $A\text{'}\left(1,5\right)$, $B\text{'}\left(-2,2\right)$ and $C\text{'}\left(-1,-1\right)$.