Suppose that a screen is $160$ pixel wide and $100$ pixels high. Recall that [[Screen Space]] has a $y$ axis that pionts downwards.
*(a).* Find the $3\times 3$ [[../Homogeneous Coordinates|Homogeneous Coordinates]] [[../Matrix]] that maps the [[Screen Space#Rectangle|Screen Space Rectangle]] to the [[Standard Square]].
$\huge
S_{\left< -\frac{1}{80}, -\frac{1}{50} \right>} \cdot T_{\left< -80,-50 \right>} =
\boxed{
\mat{
\frac{1}{80} & 0 & -1 \\
0 & -\frac{1}{50} & 1 \\
0 & 0 & 1
}} = S_{c}
$
*(b).* Find the [[Point]] inside of the [[Standard Square]] that corresponds to the [[../Point|Point]] with screen coordinates $(130, 30)$
$\huge
S_{c}\mat{130\\30\\1} = \mat{ \frac{5}{8} \\\frac{2}{5} \\ 1 }
$
*(c).* Find the [[Point]] inside the standard square that corresponds to the [[Point]] with screen coordinates $(70, 70)$
$\huge
S_{c}\mat{70\\70\\1} = \mat{
-\frac{1}{8}\\
-\frac{2}{5}\\
1
}
$