Calculate the distance between the following points: (10, 8) and (4, 8.4)

Let $(x_1, y_1) = (3, 1)$ and $(x_2, y_2) = (7, 6)$.

The distance $D$ between two points is given by $D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$.

The distance is $\boxed{6.4 \text{ units}}$.

2. Calculate the distance between $(10,8)$ and $(4,1)$

Let $(x_1, y_1) = (10, 8)$ and $(x_2, y_2) = (4, 1)$.

The distance $D$ between two points is given by $D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$.

The distance is $\boxed{9.2 \text{ units}}$.

3. Calculate the length of the new road from hospital $(1,1)$ to town $(6,5)$

Let $(x_1, y_1) = (1, 1)$ and $(x_2, y_2) = (6, 5)$.

The distance $D$ between two points is given by $D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$.

The length of the new road is $\boxed{6.4 \text{ units}}$.