Find the Distance Between Two Points (-1,2) and (1,6)

$(- 1, 2)$ and $(1, 6)$

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

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

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

$\sqrt{{(1 - (- 1))}^{2} + {(6 - 2)}^{2}}$

Simplify.

Multiply $- 1$ by $- 1$ .

$\sqrt{{(1 + 1)}^{2} + {(6 - 2)}^{2}}$

Add $1$ and $1$ .

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

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

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

Subtract $2$ from $6$ .

$\sqrt{4 + 4^{2}}$

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

$\sqrt{4 + 16}$

Add $4$ and $16$ .

$\sqrt{20}$

Rewrite $20$ as $2^{2} \cdot 5$ .

Factor $4$ out of $20$ .

$\sqrt{4 (5)}$

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

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

Pull terms out from under the radical.

$2 \sqrt{5}$

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{5}$

Decimal Form:

$4.47213595 \dots$