Question

Edison is located at $\left(9,3\right)$ in the coordinate system on a road map. Kettering is located at $\left(12,5\right)$ on the same map. Each side of a square on the map represents 10 miles. To the nearest mile, what is the distance between Edison and Kettering?

Short answer

The distance between Edison and Kettering, to the nearest mile, is36 miles.

Step-by-step solution

Step 1. Given Information.

Given, Edison is located at $\left(9,3\right)$ in the coordinate system on a road map. Kettering is located at $\left(12,5\right)$ on the same map. Each side of a square on the map represents 10 miles. The distance between Edison and Kettering is to be determined, to the nearest mile.

Step 2. Calculation.

The distance between the two points $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ is $d=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}$

Here, $\left(x_1,y_1\right)=\left(9,3\right)$ and $\left(x_2,y_2\right)=\left(12,5\right)$

Plugging the values and simplifying:

$\begin{array}{l}d=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2}\\ d=\sqrt{{\left(12-9\right)}^2+{\left(5-3\right)}^2}\\ d=\sqrt{{\left(3\right)}^2+{\left(2\right)}^2}\\ d=\sqrt{9+4}\\ d=\sqrt{13}\\ d=3.61\end{array}$

Given each unit represents 10 miles.

Hence,

$\begin{array}{l}d=3.61\times 10\\ d=36.1\text{miles}\\ d=36\text{miles}\end{array}$

Step 3. Conclusion.

Hence, the distance between Edison and Kettering, to the nearest mile, is 36 miles.