Question

Use a transformation matrix to find the image of $D(-10,1)$ after a reflection across the y-axis.

• A. $(10,-1)$
• B. $(-10,-1)$
• C. $(-10,1)$
• D. $(10,1)$

Answer 1

Answer: (D)

$(10,1)$

Reflection about Y axis

$\theta =180°$

Both side Y co ordinate is positive and X co ordinate is positive on $1$ side and negative on other

Reflection matric$=\left[\begin{array}{cc}\cos 180& \sin 180\\ \sin 180& -\cos 180\end{array}\right]$

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

Required reflection$\left[\begin{array}{cc}-10& 1\end{array}\right]\left[\begin{array}{cc}-1& 0\\ 0& 1\end{array}\right]=\left[\begin{array}{cc}10& 1\end{array}\right]$

Option D