Question

Use a transformation matrix to find the image of $D(-7,6)$ after a rotation of ${180}^0$ counterclockwise around the origin.

• A. $(7,6)$
• B. $(-7,-6)$
• C. $(7,-6)$
• D. $(-7,6)$

Answer 1

The correct option is C $(7,-6)$

The transformation matrix for rotation is $\left[\begin{array}{cc}cos\theta & -sin\theta \\ sin\theta & cos\theta \end{array}\right]$

For $\theta ={180}^0$ , the transformation matrix will be $\left[\begin{array}{cc}-1& 0\\ 0& -1\end{array}\right]$

So the image of point $(-7,6)$ is $\left[\begin{array}{cc}-1& 0\\ 0& -1\end{array}\right]\left[\begin{array}{c}-7\\ 6\end{array}\right]=\left[\begin{array}{c}7\\ -6\end{array}\right]$

Therefore the correct option is $C$