Question

Triangle $DEF$ with vertices $D\left(1,4\right),\text{E}\left(2,-5\right),\text{and}F\left(-6,-6\right)$ is translated 4 units left and 2 units up.

12. Write the translation matrix.

Short answer

The translation matrix is$\left[\begin{array}{ccc}-4& -4& -4\\ 2& 2& 2\end{array}\right]$

Step-by-step solution

- Write general translation matrix

Since, an ordered pair is represented by a column matrix and triangle has 3 ordered pair on vertices so required matrix has 2 rows and 3 columns.

If the matrix is translated to x units right or left then x is added or subtracted from first row respectively.

If the matrix is translated to y units up or down then y is added or subtracted from second row respectively.

Thus translation matrix is of the form

$\left[\begin{array}{ccc}x& x& x\\ y& y& y\end{array}\right]$

- Find value of x and y

As the triangle is translated 4 units left, so $x=-4$

As the triangle is translated 2 units op, so $y=2$

- Find translated matrix

Substitute $-4$ for x and 2 for y in general translated matrix gives required matrix

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