Find the Distance Between Two Points (-5,-9) and (-8,0)

$(- 5, - 9)$ and $(- 8, 0)$

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.

$\sqrt{{((- 8) - (- 5))}^{2} + {(0 - (- 9))}^{2}}$

Step 3

Simplify.

Multiply $- 1$ by $- 5$ .

$\sqrt{{(- 8 + 5)}^{2} + {(0 - (- 9))}^{2}}$

Add $- 8$ and $5$ .

$\sqrt{{(- 3)}^{2} + {(0 - (- 9))}^{2}}$

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

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

Multiply $- 1$ by $- 9$ .

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

Add $0$ and $9$ .

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

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