General transformations
Unlock all 5 questions & worked solutions
You're viewing a free preview. Create an account to access the complete question set, step-by-step solutions, and progress tracking.
All Questions
Access the full question set for every topic.
Worked Solutions
Step-by-step explanations for every answer.
Track Progress
Mark questions right or wrong and monitor your growth.
It's Free
No credit card required - sign up in under a minute.
Find the transformation that rotates the plane by \(90^\circ\) anticlockwise about the point \((1,2)\)
$$
\begin{aligned}
&\text{Anticlockwise rotation} =\left[\begin{array}{cr}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta\end{array}\right]=R\\
\theta&=90^{\circ} \rightarrow R=\left[\begin{array}{cc}0 & -1 \\ 1 & 0\end{array}\right]\\
&\begin{aligned}
\left[\begin{array}{l}x^{\prime} \\ y^{\prime}\end{array}\right] &=\left[\begin{array}{rr}0 & -1 \\ 1 & 0\end{array}\right]\left[\begin{array}{l}x-1 \\ y-2\end{array}\right]+\left[\begin{array}{l}1 \\ 2\end{array}\right] \\ &=\left[\begin{array}{r}-y+2 \\ x-1\end{array}\right]+\left[\begin{array}{l}1 \\ 2\end{array}\right] \\ &=\left[\begin{array}{c}-y+3 \\ x+1\end{array}\right]
\end{aligned}\end{aligned}
$$
📚 Want More Questions?
There are 4 more questions available. Create your free account to access the complete question set with detailed solutions.