Chapter 12.5, Problem 18PPSE

Solution

To find: The coordinates of image after the rotation. Then to graph the figures.

  $\left(0,0\right),\left(4,4\right),\left(8,4\right),\left(6,2\right)$

Given information:

Given,coordinates of a figure and the rotation required are:

  $\left[\begin{array}{cccc}0& 4& 8& 6\\ 0& 4& 4& 2\end{array}\right];360°$

Calculation:

The rotation of a figure by 360° is given by multiplying the matrix with:

  $\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$

The coordinates after the rotation are given by:

  $\begin{array}{l}\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]\left[\begin{array}{cccc}0& 4& 8& 6\\ 0& 4& 4& 2\end{array}\right]=\left[\begin{array}{cccc}\left(1\right)\left(0\right)+\left(0\right)\left(0\right)& \left(1\right)\left(4\right)+\left(0\right)\left(4\right)& \left(1\right)\left(8\right)+\left(0\right)\left(4\right)& \left(1\right)\left(6\right)+\left(0\right)\left(2\right)\\ \left(0\right)\left(0\right)+\left(1\right)\left(0\right)& \left(0\right)\left(4\right)+\left(1\right)\left(4\right)& \left(0\right)\left(8\right)+\left(1\right)\left(4\right)& \left(0\right)\left(6\right)+\left(1\right)\left(2\right)\end{array}\right]\\ \left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]\left[\begin{array}{cccc}0& 4& 8& 6\\ 0& 4& 4& 2\end{array}\right]=\left[\begin{array}{cccc}0+0& 4+0& 8+0& 6+0\\ 0+0& 0+4& 0+4& 0+2\end{array}\right]\\ \left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]\left[\begin{array}{cccc}0& 4& 8& 6\\ 0& 4& 4& 2\end{array}\right]=\left[\begin{array}{cccc}0& 4& 8& 6\\ 0& 4& 4& 2\end{array}\right]\end{array}$

The coordinates after rotation are:

  $\left(0,0\right),\left(4,4\right),\left(8,4\right),\left(6,2\right)$

Conclusion:

  $\left(0,0\right),\left(4,4\right),\left(8,4\right),\left(6,2\right)$