In the rectangular coordinate plane, the distance between points $\mathrm{A}(\mathrm{a}, \mathrm{b})$ and $\mathrm{B}(\mathrm{c}, \mathrm{d})$ is calculated using the formula
$$|AB| = \sqrt{(c-a)^{2} + (d-b)^{2}}$$
On the scaled map below; the coordinates of points $\mathrm{A}$, $\mathrm{B}$ and $\mathrm{C}$ in the rectangular coordinate plane are given according to a certain unit of length.
A map program that calculates the distance between two points calculates the distance shown by the blue line between points $\mathrm{A}(2,8)$ and $\mathrm{B}(10,14)$ as 6 kilometers.
Accordingly, what distance in kilometers does this map program calculate for the blue line distance between points A and C?
A) 7.8\\
B) 8.1\\
C) 9.6\\
D) 10.4\\
E) 11.7