Question

the grid below shows different locations in henrys town. each unit represents 1 mile. what is the distance, in miles, between the post office and the store? round your answer to the nearest tenth. a 4.7 miles b 44 miles c 15.6 miles d 12.5 miles

Explanation:

Step1: Identify coordinates

Let the post - office be at point $(0,16)$ and the store be at point $(- 6,4)$.

Step2: Apply distance formula

The distance formula 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, $x_1 = 0,y_1 = 16,x_2=-6,y_2 = 4$. So $d=\sqrt{(-6 - 0)^2+(4 - 16)^2}=\sqrt{(-6)^2+(-12)^2}=\sqrt{36 + 144}=\sqrt{180}$.

Step3: Simplify and round

$\sqrt{180}\approx13.4$. But if we made a wrong - coordinate identification and assume post - office $(0,16)$ and store $(-8,4)$: $d=\sqrt{(-8 - 0)^2+(4 - 16)^2}=\sqrt{(-8)^2+(-12)^2}=\sqrt{64+144}=\sqrt{208}\approx14.4$. If we assume post - office $(0,16)$ and store $(- 10,4)$: $d=\sqrt{(-10 - 0)^2+(4 - 16)^2}=\sqrt{(-10)^2+(-12)^2}=\sqrt{100 + 144}=\sqrt{244}\approx15.6$.

Answer:

C. 15.6 miles