-If an open path consisting solely of a vertical line from \tcode{vector_2d(20.0, 20.0)} to \tcode{vector_2d(20.0, 60.0)} is to be composed to the \underlyingsurface, the Line Cap is \tcode{line_cap::butt}, the Line Width is \tcode{12.0}, and the Transformation Matrix is \tcode{matrix_2d::init_scale(0.5, 1.0)}, then the line will end up being composed within the area \tcode{rectangle( \{ 7.0, 20.0 \}, \{ 13.0, 60.0 \} )} on the \underlyingsurface. The Transformation Matrix causes the center of the \xaxis of the line to move from \tcode{20.0} to \tcode{10.0} and then causes the horizontal width of the line to be reduced from \tcode{12.0} to \tcode{6.0}.
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