Find the Distance Between Two Points (8,-8) and (-1,-5)

$(8, - 8)$ and $(- 1, - 5)$

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.

$\sqrt{{((- 1) - 8)}^{2} + {((- 5) - (- 8))}^{2}}$

Step 3

Simplify.

Subtract $8$ from $- 1$ .

$\sqrt{{(- 9)}^{2} + {((- 5) - (- 8))}^{2}}$

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

$\sqrt{81 + {((- 5) - (- 8))}^{2}}$

Multiply $- 1$ by $- 8$ .

$\sqrt{81 + {(- 5 + 8)}^{2}}$

Add $- 5$ and $8$ .

$\sqrt{81 + 3^{2}}$

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

$\sqrt{81 + 9}$

Add $81$ and $9$ .

$\sqrt{90}$

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