Chapter 4, Problem 23SGR

To determine

To find: The coordinates of the image after transformation.

Answer to Problem 23SGR

The new coordinate of the image after transformation are,

  $A\left(2,12\right),B\left(16,12\right),C\left(2,4\right),D\left(16,4\right)$ .

Explanation of Solution

Given:

The given image is shown in Figure 1

  

Figure 1

Calculation:

Consider the given diagram and write then write the coordinates of the rectangle in the matrix forma as,

  $\left[\begin{array}{cccc}1& 8& 1& 8\\ 6& 6& 2& 2\end{array}\right]$

Apply dilation scale of factor 2 on the above matrix as,

  $\left[\begin{array}{cccc}2& 16& 2& 16\\ 12& 12& 4& 4\end{array}\right]$

Then, the new coordinates of the triangle are,

  $\begin{array}{l}A\left(2,12\right)\\ B\left(16,12\right)\\ C\left(2,4\right)\\ D\left(16,4\right)\end{array}$