Invariant points and linesAQA A-Level Further Maths: Mind map

Exam questions on Invariant points and lines

1. The transformation $T$ of the plane has matrix $\mathbf{M}=\begin{pmatrix}1&2\\0&3\end{pmatrix}$.
   Show that the line $y=2x$ is not invariant under $T$.2 marks
2. The matrix $\mathbf{N}=\begin{pmatrix}-1&0\\0&1\end{pmatrix}$ represents a reflection in the $y$-axis.
   Find the equation of the image of the line $y=2x+3$ under the reflection, and hence state whether this line is invariant.2 marks
3. The matrix $\mathbf{S}=\begin{pmatrix}2&-1\\1&0\end{pmatrix}$ represents a transformation $S$ of the plane.
   Find the invariant points of $S$.3 marks