2D Scaling

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Scaling a point with homogeneous coordinates $(x, y, w)$ by a factor $s_\mathrm{x}$ along the X-axis and a factor $s_\mathrm{y}$ along the Z-axis is achieved by the following matrix multiplication:

$\begin{bmatrix} s_\mathrm{x} & 0 & 0 \\ 0 & s_\mathrm{y} & 0 \\ 0 & 0 & 1 \\ \end{bmatrix} \cdot \begin{bmatrix} x \\ y \\ w \\ \end{bmatrix}$

Example

Scaling $P(3, 5)$ by 2 along the X-axis:

$\begin{bmatrix} 2 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ \end{bmatrix} \cdot \begin{bmatrix} 3 \\ 5 \\ 1 \\ \end{bmatrix} = \begin{bmatrix} 6 \\ 10 \\ 1 \\ \end{bmatrix}$