Question

11 multiple choice 1 point at noon on a certain day, train a is 14 miles east and 16 miles north of the depot. at the same time, train b is 12 miles west and 14 miles south of the depot. find the distance between trains. round your answer to the nearest tenth of a mile. 40.3 miles 42.6 miles 40.0 miles 39.4 miles 39.2 miles

Explanation:

Step1: Find the difference in x - coordinates

The x - coordinate of Train A is 14 (east is positive) and of Train B is - 12 (west is negative). The difference $\Delta x=14-(-12)=14 + 12=26$.

Step2: Find the difference in y - coordinates

The y - coordinate of Train A is 16 (north is positive) and of Train B is - 14 (south is negative). The difference $\Delta y=16-(-14)=16 + 14=30$.

Step3: Use the distance formula

The distance $d$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $d=\sqrt{\Delta x^{2}+\Delta y^{2}}=\sqrt{26^{2}+30^{2}}=\sqrt{676 + 900}=\sqrt{1576}$.

Step4: Calculate the square - root and round

$\sqrt{1576}\approx39.7$.

Answer:

E. 39.7 miles