Find the Distance Between Two Points (-7,-5) and (-3,4)

$(- 7, - 5)$ and $(- 3, 4)$

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.

$\sqrt{{((- 3) - (- 7))}^{2} + {(4 - (- 5))}^{2}}$

Simplify.

Multiply $- 1$ by $- 7$ .

$\sqrt{{(- 3 + 7)}^{2} + {(4 - (- 5))}^{2}}$

Add $- 3$ and $7$ .

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

Raise $4$ to the power of $2$ .

$\sqrt{16 + {(4 - (- 5))}^{2}}$

Multiply $- 1$ by $- 5$ .

$\sqrt{16 + {(4 + 5)}^{2}}$

Add $4$ and $5$ .

$\sqrt{16 + 9^{2}}$

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

$\sqrt{16 + 81}$

Add $16$ and $81$ .

$\sqrt{97}$

The result can be shown in multiple forms.

Exact Form:

$\sqrt{97}$

Decimal Form:

$9.84885780 \dots$