Q45. - Algebra 2

Question

For Exercises 45-47, use the following information.

Triangle $\mathbf{ABC}$with vertices $\mathbf{A}\left(\mathbf{0}\mathbf{,}\mathbf{2}\right)$, $\mathbf{B}\left(\mathbf{-}\mathbf{3}\mathbf{,}\mathbf{-}\mathbf{1}\right)$ and $\mathbf{C}\left(\mathbf{-}\mathbf{2}\mathbf{,}\mathbf{-}\mathbf{4}\right)$ is translated 1 unit right and 3 units up.

45. Write the translation matrix.

Step-by-Step Solution

Answer

The translation matrix is: $\left[\begin{array}{ccc}1& 1& 1\\ 3& 3& 3\end{array}\right]$

Step 1 ­- Description of step.

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.

Step 2 ­- Write the vertex matrix for the triangle ABC.

The vertex matrix for the triangle \[ABC\] is given by:

$\left[\begin{array}{ccc}0& -3& -2\\ 2& -1& -4\end{array}\right]$

Step 3 ­- Description of step.

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:$\left[\begin{array}{ccc}1& 1& 1\\ 3& 3& 3\end{array}\right]$