Question

On a park ma, the ranger station is located (2.5, 3.5) and the nature center is located at (0.5, 4). Each unit in the map is equal to 0.5 mile. What is the approximate distance between the ranger station and the nature center?

Answer 1

Answer: $1.0308\text{ miles}$

Step-by-step explanation:

Distance between two points $(x_1,y_1)$ and $(x_2,y_2)$ :

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

The ranger station is located (2.5, 3.5) and the nature center is located at (0.5, 4) .

Distance between ranger station and nature center

$\sqrt{(2.5-0.5)^2+(3.5-4)^2}=\sqrt{2^2+(-0.5)^2}\\\\=\sqrt{4+0.25}\\\\=\sqrt{4.25}\\\\=2.0616\text{ units}$

Each unit in the map is equal to 0.5 mile.

Hence, Distance between ranger station and nature center  = $2.0616\times0.5=1.0308\text{ miles}$