Q42. - Algebra 2

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?

Step-by-Step Solution

Answer

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

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.