Question

graph units are in kilometers. what is the distance from diegos ship to the closest island? round the final answer to the nearest tenth of a kilometer. do not round intermediate calculations. km

Explanation:

Step1: Identify coordinates

Let Diego's ship be at the origin $(0,0)$. Island B is at $(2, - 6)$ and Island C is at $(-6,-7)$. Island at $(-3,1)$ is also visible.

Step2: Use distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.
For Island B: $d_B=\sqrt{(2 - 0)^2+(-6 - 0)^2}=\sqrt{4 + 36}=\sqrt{40}=2\sqrt{10}$
For Island C: $d_C=\sqrt{(-6 - 0)^2+(-7 - 0)^2}=\sqrt{36+49}=\sqrt{85}$
For the island at $(-3,1)$: $d=\sqrt{(-3 - 0)^2+(1 - 0)^2}=\sqrt{9 + 1}=\sqrt{10}$

Step3: Compare distances

We have $d_B = 2\sqrt{10}\approx2\times3.162 = 6.324$, $d_C=\sqrt{85}\approx9.22$ and $\sqrt{10}\approx3.162$.

Answer:

$3.2$