Find the Distance Between Two Points (0,8) and (4,0)

$(0, 8)$ and $(4, 0)$

Step 1

Use the distance formula to determine the distance between the two points.

$Distance = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}$

Step 2

Substitute the actual values of the points into the distance formula.

$\sqrt{{(4 - 0)}^{2} + {(0 - 8)}^{2}}$

Step 3

Simplify.

Subtract $0$ from $4$ .

$\sqrt{4^{2} + {(0 - 8)}^{2}}$

Raise $4$ to the power of $2$ .

$\sqrt{16 + {(0 - 8)}^{2}}$

Subtract $8$ from $0$ .

$\sqrt{16 + {(- 8)}^{2}}$

Raise $- 8$ to the power of $2$ .

$\sqrt{16 + 64}$

Add $16$ and $64$ .

$\sqrt{80}$

Rewrite $80$ as $4^{2} \cdot 5$ .

Factor $16$ out of $80$ .

$\sqrt{16 (5)}$

Rewrite $16$ as $4^{2}$ .

$\sqrt{4^{2} \cdot 5}$

Pull terms out from under the radical.

$4 \sqrt{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$4 \sqrt{5}$

Decimal Form:

$8.94427190 \dots$

Step 5