Question

use a transformation matrix to find the image of ( r(9,4) ) after a translation of 10 units left and 1 unit down.

Explanation:

Step1: Set up the translation matrix

The translation matrix for a translation of \(a\) units left (where \(a = 10\)) and \(b\) units down (where \(b=1\)) is \(

$$\begin{bmatrix}1&0&- 10\\0&1&-1\\0&0&1\end{bmatrix}$$

\), and the coordinate matrix of the point \(R(9,4)\) is \(

$$\begin{bmatrix}9\\4\\1\end{bmatrix}$$

\).

Step2: Multiply the matrices

$$
LATEXBLOCK2
$$

Answer:

The image of the point \(R(9,4)\) is \((-1,3)\)