Find the Distance Between Two Points (0,-4) and (6,2)

$(0, - 4)$ and $(6, 2)$

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.

$\sqrt{{(6 - 0)}^{2} + {(2 - (- 4))}^{2}}$

Step 3

Simplify.

Subtract $0$ from $6$ .

$\sqrt{6^{2} + {(2 - (- 4))}^{2}}$

Raise $6$ to the power of $2$ .

$\sqrt{36 + {(2 - (- 4))}^{2}}$

Multiply $- 1$ by $- 4$ .

$\sqrt{36 + {(2 + 4)}^{2}}$

Add $2$ and $4$ .

$\sqrt{36 + 6^{2}}$

Raise $6$ to the power of $2$ .

$\sqrt{36 + 36}$

Add $36$ and $36$ .

$\sqrt{72}$

Rewrite $72$ as $6^{2} \cdot 2$ .

Factor $36$ out of $72$ .

$\sqrt{36 (2)}$

Rewrite $36$ as $6^{2}$ .

$\sqrt{6^{2} \cdot 2}$

Pull terms out from under the radical.

$6 \sqrt{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$6 \sqrt{2}$

Decimal Form:

$8.48528137 \dots$

Step 5