Question

use matrices to determine the coordinates of the vertices of the translated figure. Triangle DEF with vertex matrix [7 -9 -1 -7 -3 -7] translated 1 unites left and 4 units down.

Answer 1

(6, -11), (-10, -7) and (-2, -11)

Explanation:

Coordinates of a triangle are represented in the form of a matrix as,

`\begin{bmatrix}x_1 & x_2 & x_3\\ y_1 & y_2 & y_3\end{bmatrix}`

If the given triangle is shifted by 1 unit left and 4 units down,

Translation of vertices in the matrix form will be,

`\begin{bmatrix}x_1 & x_2 & x_3\\ y_1 & y_2 & y_3\end{bmatrix}+\begin{bmatrix}-1 & -1 & -1\\ -4 & -4 & -4\end{bmatrix}`

For a triangle having vertices (7, -7), (-9, -3) and (-1, -7) when shifted 1 units left and 4 units down will be,

`\begin{bmatrix}7 & -9 & -1\\ -7 & -3 & -7\end{bmatrix}+\begin{bmatrix}-1 & -1 & -1\\ -4 & -4 & -4\end{bmatrix}`

=
`\begin{bmatrix}7-1 & -9-1 & -1-1\\ -7-4 & -3-4 & -7-4\end{bmatrix}`

=
`\begin{bmatrix}6 & -10 & -2\\ -11 & -7 & -11\end{bmatrix}`

Coordinates of the triangle after the translation will be,

(6, -11), (-10, -7) and (-2, -11)