If $\alpha = 1 + \sum _ { r = 1 } ^ { 6 } ( - 3 ) ^ { r - 1 } \quad { } ^ { 12 } \mathrm { C } _ { 2 r - 1 }$, then the distance of the point $( 12 , \sqrt { 3 } )$ from the line $\alpha x - \sqrt { 3 } y + 1 = 0$ is $\_\_\_\_$.
If $\alpha = 1 + \sum _ { r = 1 } ^ { 6 } ( - 3 ) ^ { r - 1 } \quad { } ^ { 12 } \mathrm { C } _ { 2 r - 1 }$, then the distance of the point $( 12 , \sqrt { 3 } )$ from the line $\alpha x - \sqrt { 3 } y + 1 = 0$ is $\_\_\_\_$.