Question

modeling real life the locations of several sites in a forest are shown in the coordinate plane. approximate each distance to the nearest tenth.
a. how far is the cabin from the peak? 5.8 km
b. how far is the fire tower from the lake? 8.0 km
c. how far is the lake from the peak? km

Explanation:

Step1: Identify coordinates

Assume cabin is at $(-3,0)$, peak is at $(0, - 5.5)$, lake is at $(5,0)$.

Step2: Use distance formula $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$ for lake and peak

For lake $(x_1,y_1)=(5,0)$ and peak $(x_2,y_2)=(0,-5.5)$. Then $d=\sqrt{(0 - 5)^2+(-5.5 - 0)^2}=\sqrt{(-5)^2+(-5.5)^2}=\sqrt{25 + 30.25}=\sqrt{55.25}$.

Step3: Calculate square - root and round

$\sqrt{55.25}\approx7.4$ km.

Answer:

7.4 km