Answer :
Answer: [tex]1.0308\text{ miles}[/tex]
Step-by-step explanation:
Distance between two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] :
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
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
[tex]\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}[/tex]
Each unit in the map is equal to 0.5 mile.
Hence, Distance between ranger station and nature center = [tex]2.0616\times0.5=1.0308\text{ miles}[/tex]