Answer:
[tex]\large\boxed{\sqrt{80}=4\sqrt5}[/tex]
Step-by-step explanation:
Method 1:
The formula of a distance between two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
We have the points (-4, 1) and (4, 5). Substitute:
[tex]d=\sqrt{(4-(-4))^2+(5-1)^2}=\sqrt{8^2+4^2}=\sqrt{64+16}=\sqrt{80}[/tex]
[tex]\sqrt{80}=\sqrt{16\cdot5}=\sqrt{16}\cdot\sqrt5=4\sqrt5[/tex]
Method 2:
Look at the picture.
Use the Pythagorean theorem:
[tex]leg^2+leg^2=hypotenuse^2[/tex]
We have
[tex]leg=8,\ leg=4,\ hypotenuse=x[/tex]
Substitute:
[tex]x^2=8^2+4^2\\\\x^2=64+16\\\\x^2=80\to x=\sqrt{80}\\\\x=4\sqrt5[/tex]
