Find the Distance Between Two Points (-4,-3) and (5,9)

$(- 4, - 3)$ and $(5, 9)$

Use the distance formula to determine the distance between the two points.

$Distance = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}$

Substitute the actual values of the points into the distance formula.

$\sqrt{{(5 - (- 4))}^{2} + {(9 - (- 3))}^{2}}$

Simplify.

Multiply $- 1$ by $- 4$ .

$\sqrt{{(5 + 4)}^{2} + {(9 - (- 3))}^{2}}$

Add $5$ and $4$ .

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

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

$\sqrt{81 + {(9 - (- 3))}^{2}}$

Multiply $- 1$ by $- 3$ .

$\sqrt{81 + {(9 + 3)}^{2}}$

Add $9$ and $3$ .

$\sqrt{81 + 12^{2}}$

Raise $12$ to the power of $2$ .

$\sqrt{81 + 144}$

Add $81$ and $144$ .

$\sqrt{225}$

Rewrite $225$ as $15^{2}$ .

$\sqrt{15^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$15$