IB Maths AI 3.8 Definitions

A way to represent a point $(x,y)$ as $\begin{pmatrix}x\\y\end{pmatrix}$ so a matrix can act on it.

A transformation about the origin that scales both coordinates by the same factor $k$, using $\begin{pmatrix}k&&0\\0&&k\end{pmatrix}$

A transformation that multiplies the $x$-coordinate by a scale factor $k$ while leaving the $y$-coordinate unchanged, using $\begin{pmatrix}k&&0\\0&&1\end{pmatrix}$

A transformation that flips points in a line (such as an axis), reversing orientation while preserving distances.

A transformation about the origin through angle $\theta$ anticlockwise, represented by $\begin{pmatrix}\cos\theta&&-\sin\theta\\\sin\theta&&\cos\theta\end{pmatrix}$

A change to a geometric object that can alter its position, orientation, or size.

A vector $\begin{pmatrix}e\\f\end{pmatrix}$ that shifts every point by the same amount, giving $\begin{pmatrix}x'\\y'\end{pmatrix}=\begin{pmatrix}x\\y\end{pmatrix}+\begin{pmatrix}e\\f\end{pmatrix}$

A transformation that multiplies the $y$-coordinate by a scale factor $k$ while leaving the $x$-coordinate unchanged, using $\begin{pmatrix}1&&0\\0&&k\end{pmatrix}$