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:
\[ \begin{bmatrix}
s_\mathrm{x} & 0 & 0 \\
0 & s_\mathrm{y} & 0 \\
0 & 0 & 1 \\
\end{bmatrix}
\cdot
\begin{bmatrix}
x \\
y \\
w \\
\end{bmatrix}\]
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Example
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Scaling \(P(3, 5)\) by 2 along the X-axis:
\[ \begin{bmatrix}
2 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1 \\
\end{bmatrix}
\cdot
\begin{bmatrix}
3 \\
5 \\
1 \\
\end{bmatrix}
=
\begin{bmatrix}
6 \\
10 \\
1 \\
\end{bmatrix}\]
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