Find the Distance Between Two Points (-9,-4) and (0,-7)

$(- 9, - 4)$ and $(0, - 7)$

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.

$\sqrt{{(0 - (- 9))}^{2} + {((- 7) - (- 4))}^{2}}$

Step 3

Simplify.

Multiply $- 1$ by $- 9$ .

$\sqrt{{(0 + 9)}^{2} + {((- 7) - (- 4))}^{2}}$

Add $0$ and $9$ .

$\sqrt{9^{2} + {((- 7) - (- 4))}^{2}}$

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

$\sqrt{81 + {((- 7) - (- 4))}^{2}}$

Multiply $- 1$ by $- 4$ .

$\sqrt{81 + {(- 7 + 4)}^{2}}$

Add $- 7$ and $4$ .

$\sqrt{81 + {(- 3)}^{2}}$

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