Use the distance formula between $(2,3)$ and $(8,11)$:

So the length of the path is $10$ map units.

To find the point halfway between $(3,2)$ and $(9,10)$, use the midpoint formula:

Substitute the coordinates:

So the repair kiosk should be placed at $(6,6)$.

Use the midpoint formula. For endpoints $A(x_1,y_1)$ and $B(x_2,y_2)$, the midpoint is

Here, the $x$-coordinate of the midpoint is 2, so

Multiply both sides by 2:

Then add 3 to both sides:

Therefore, the correct answer is $7$.

Use the distance formula, which is based on the horizontal and vertical changes between the points. From $(3,-2)$ to $(9,6)$, the change in $x$ is $9-3=6$ and the change in $y$ is $6-(-2)=8$. So the distance is

Therefore, the equivalent expression is $\sqrt{6^2+8^2}$.

The slope of a line through two points is found with $\frac{y_2-y_1}{x_2-x_1}$. Using $(1,4)$ and $(5,10)$ gives

So the slope of the line is $\frac{3}{2}$.