3.9 Matrix transformationsIB Maths: Applications and Interpretation HL: Mind map

Exam questions on 3.9 Matrix transformations

1. Transformation $T$ is represented by the matrix $\mathbf{M}=\begin{pmatrix}0 & -1 \\ 1 & 0\end{pmatrix}$, so that a point $(x,y)$ maps to the point with position vector $\mathbf{M}\begin{pmatrix}x \\ y\end{pmatrix}$.
   $T$ is followed by a reflection in the $x$-axis, which has matrix $\mathbf{R}=\begin{pmatrix}1 & 0 \\ 0 & -1\end{pmatrix}$. Find the single matrix that represents this combined transformation.2 marks
2. Triangle $S$ has area $8$ cm$^2$. It is transformed by the matrix $\mathbf{N}=\begin{pmatrix}3 & 1 \\ 2 & 2\end{pmatrix}$ to give triangle $S'$.
   $S'$ is then enlarged by scale factor $2$, centre the origin, to give triangle $S''$. Find the area of $S''$.2 marks
3. A transformation $U$ maps a point with position vector $\begin{pmatrix}x \\ y\end{pmatrix}$ to $\begin{pmatrix}2 & 0 \\ 0 & 2\end{pmatrix}\begin{pmatrix}x \\ y\end{pmatrix}+\begin{pmatrix}1 \\ -3\end{pmatrix}$. Triangle $ABC$ has vertices $A(1,2)$, $B(4,2)$ and $C(1,6)$, with lengths in cm.
   Find the coordinates of the images $A'$, $B'$ and $C'$ of the vertices of triangle $ABC$ under $U$.3 marks