Solution:

$2 \mathrm{Y}-\mathrm{X}-4=0$

$\mathrm{Y}=0.5 \mathrm{X}+2$

$\tan \theta=\mathrm{m}=0.5$

$\therefore y=m x+c$

$\theta=26.56^{\circ}$

Steps:-

1. $Tr =$ Translate point $(0,-2)$ to origin $\mathrm{O}(0,0)$

2. $\mathrm{R}=$ Rotate the line about origin by $. \theta=-26.56^{\circ}$

3. Reflect the object about $\mathrm{x}$ -axis $(\mathrm{Mx})$
4. Inverse Rotate the line about origin by $. \theta=26.56^{\circ}$
5. $\operatorname{Tr}^{-1}=$ Inverse Translation to original position a $(0,2)$

$[\mathrm{T}]=(\mathrm{Tr})(\mathrm{R})(\mathrm{Mx})(R)^{-1}(T)^{-1}$

$[\mathrm{T}]=\left[\begin{array}{ccc}{1} & {0} & {0} \\ {0} & {1} & {0} \\ {t x} & {t y} & {1}\end{array}\right] \times \left[\begin{array}{ccc}{\cos -26.56} & {\sin -26.56} & {0} \\ {-\sin -26.56} & {\cos -26.56} & {0} \\ {0} & {0} & {1}\end{array}\right]\times \left[\begin{array}{ccc}{1} & {0} & {0} \\ {0} & {-1} & {0} \\ {0} & {0} & {1}\end{array}\right] \times \left[\begin{array}{ccc}{\cos 26.56} & {\sin 26.56} & {0} \\ {-\sin 26.56} & {\cos 26.56} & {0} \\ {0} & {0} & {1}\end{array}\right] \times \left[\begin{array}{ccc}{1} & {0} & {0} \\ {0} & {1} & {0} \\ {t x} & {t y} & {1}\end{array}\right]$

$[\mathrm{T}]=\left[\begin{array}{ccc}{1} & {0} & {0} \\ {0} & {1} & {0} \\ {0} & {-2} & {1}\end{array}\right] \times\left[\begin{array}{ccc}{\cos -26.56} & {\sin -26.56} & {0} \\ {-\sin -26.56} & {\cos -26.56} & {0} \\ {0} & {0} & {1}\end{array}\right]\times \left[\begin{array}{ccc}{1} & {0} & {0} \\ {0} & {-1} & {0} \\ {0} & {0} & {1}\end{array}\right] \times\left[\begin{array}{ccc}{\cos 26.56} & {\sin 26.56} & {0} \\ {-\sin 26.56} & {\cos 26.56} & {0} \\ {0} & {0} & {1}\end{array}\right] \times \left[\begin{array}{ccc}{1} & {0} & {0} \\ {0} & {1} & {0} \\ {0} & {2} & {1}\end{array}\right]$

$[\mathrm{T}]=\left[\begin{array}{ccc}{0.6001} & {0.7995} & {0} \\ {0.7995} & {-0.6} & {0} \\ {-1.6} & {3.2} & {1}\end{array}\right]$

$\left[\begin{array}{l}{A^{\prime}} \\ {B^{\prime}} \\ {C^{\prime}}\end{array}\right]=\left[\begin{array}{lll}{2} & {4} & {1} \\ {4} & {6} & {1} \\ {2} & {6} & {1}\end{array}\right] \times \left[\begin{array}{ccc}{0.6001} & {0.7995} & {0} \\ {0.7995} & {-0.6} & {0} \\ {-1.6} & {3.2} & {1}\end{array}\right]$

$\left[\begin{array}{l}{A^{\prime}} \\ {B^{\prime}} \\ {C^{\prime}}\end{array}\right]=\left[\begin{array}{lll}{2.8} & {2.4} & {1} \\ {5.6} & {2.8} & {1} \\ {4.4} & {1.2} & {1}\end{array}\right]$

$\therefore A^{\prime}=2.8,2.4$

$\therefore B^{\prime}=5.6,2.8$

$\therefore C^{\prime}=4.4,1.2$