Find the Distance Between Two Points (-5,-4) and (4,1)

$(- 5, - 4)$ and $(4, 1)$

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

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

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

$\sqrt{{(4 - (- 5))}^{2} + {(1 - (- 4))}^{2}}$

Simplify.

Multiply $- 1$ by $- 5$ .

$\sqrt{{(4 + 5)}^{2} + {(1 - (- 4))}^{2}}$

Add $4$ and $5$ .

$\sqrt{9^{2} + {(1 - (- 4))}^{2}}$

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

$\sqrt{81 + {(1 - (- 4))}^{2}}$

Multiply $- 1$ by $- 4$ .

$\sqrt{81 + {(1 + 4)}^{2}}$

Add $1$ and $4$ .

$\sqrt{81 + 5^{2}}$

Raise $5$ to the power of $2$ .

$\sqrt{81 + 25}$

Add $81$ and $25$ .

$\sqrt{106}$

The result can be shown in multiple forms.

Exact Form:

$\sqrt{106}$

Decimal Form:

$10.29563014 \dots$