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? km b. how far is the fire tower from the lake? km

Explanation:

Step1: Identify coordinates

Let the cabin be at point $C(-3,0)$, the peak be at point $P(0, - 5)$, the fire - tower be at point $F(0,7)$ and the lake be at point $L(5,0)$.

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

For the distance between the cabin $C(-3,0)$ and the peak $P(0,-5)$:
$x_1=-3,y_1 = 0,x_2=0,y_2=-5$
$d_{CP}=\sqrt{(0 - (-3))^2+(-5 - 0)^2}=\sqrt{3^2+(-5)^2}=\sqrt{9 + 25}=\sqrt{34}\approx5.8$ km

Step3: Use distance formula for part b

For the distance between the fire - tower $F(0,7)$ and the lake $L(5,0)$:
$x_1=0,y_1 = 7,x_2=5,y_2=0$
$d_{FL}=\sqrt{(5 - 0)^2+(0 - 7)^2}=\sqrt{25+49}=\sqrt{74}\approx8.6$ km

Answer:

a. $5.8$ km
b. $8.6$ km