Find the Distance Between Two Points (-2,-8) , (1,1)

$(- 2, - 8)$ , $(1, 1)$

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.

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

Step 3

Simplify.

Multiply $- 1$ by $- 2$ .

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

Add $1$ and $2$ .

$\sqrt{3^{2} + {(1 - (- 8))}^{2}}$

Raise $3$ to the power of $2$ .

$\sqrt{9 + {(1 - (- 8))}^{2}}$

Multiply $- 1$ by $- 8$ .

$\sqrt{9 + {(1 + 8)}^{2}}$

Add $1$ and $8$ .

$\sqrt{9 + 9^{2}}$

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

$\sqrt{9 + 81}$

Add $9$ and $81$ .

$\sqrt{90}$

Rewrite $90$ as $3^{2} \cdot 10$ .

Factor $9$ out of $90$ .

$\sqrt{9 (10)}$

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

$\sqrt{3^{2} \cdot 10}$

Pull terms out from under the radical.

$3 \sqrt{10}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt{10}$

Decimal Form:

$9.48683298 \dots$

Step 5