Question

use a transformation matrix to find the image of ( w(-8,0) ) after a dilation with a scale factor of ( \frac{1}{4} ) centered at the origin.

Explanation:

Step1: Write the transformation matrix

The transformation matrix for a dilation centered at the origin with scale factor \(k\) is \(

$$\begin{bmatrix}k&0\\0&k\end{bmatrix}$$

\). Here \(k = \frac{1}{4}\), so the matrix is \(

$$\begin{bmatrix}\frac{1}{4}&0\\0&\frac{1}{4}\end{bmatrix}$$

\).

Step2: Write the coordinate matrix of the point

The coordinate matrix of the point \(W(-8,0)\) is \(

$$\begin{bmatrix}-8\\0\end{bmatrix}$$

\).

Step3: Multiply the matrices

$$
LATEXBLOCK3
$$

Answer:

\((-2,0)\)