Find the Distance Between Two Points (-1,0) , (8,6)

$(- 1, 0)$ , $(8, 6)$

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.

$\sqrt{{(8 - (- 1))}^{2} + {(6 - 0)}^{2}}$

Step 3

Simplify.

Multiply $- 1$ by $- 1$ .

$\sqrt{{(8 + 1)}^{2} + {(6 - 0)}^{2}}$

Add $8$ and $1$ .

$\sqrt{9^{2} + {(6 - 0)}^{2}}$

Raise $9$ to the power of $2$ .

$\sqrt{81 + {(6 - 0)}^{2}}$

Subtract $0$ from $6$ .

$\sqrt{81 + 6^{2}}$

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

$\sqrt{81 + 36}$

Add $81$ and $36$ .

$\sqrt{117}$

Rewrite $117$ as $3^{2} \cdot 13$ .

Factor $9$ out of $117$ .

$\sqrt{9 (13)}$

Rewrite $9$ as $3^{2}$ .

$\sqrt{3^{2} \cdot 13}$

Pull terms out from under the radical.

$3 \sqrt{13}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt{13}$

Decimal Form:

$10.81665382 \dots$

Step 5