Question

10 points help please!?

Answer 1

`\large\boxed{√(80)=4\sqrt5}`

Explanation:

Method 1:

The formula of a distance between two points:

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

We have the points (-4, 1) and (4, 5). Substitute:

`d=√((4-(-4))^2+(5-1)^2)=√(8^2+4^2)=√(64+16)=√(80)`

`√(80)=√(16\cdot5)=√(16)\cdot\sqrt5=4\sqrt5`

Method 2:

Look at the picture.

Use the Pythagorean theorem:

`leg^2+leg^2=hypotenuse^2`

We have

`leg=8,\ leg=4,\ hypotenuse=x`

Substitute:

`x^2=8^2+4^2\\\\x^2=64+16\\\\x^2=80\to x=√(80)\\\\x=4\sqrt5`