Find the Distance Between Two Points (-7,-13) , (10,8)

$(- 7, - 13)$ , $(10, 8)$

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.

$\sqrt{{(10 - (- 7))}^{2} + {(8 - (- 13))}^{2}}$

Simplify.

Multiply $- 1$ by $- 7$ .

$\sqrt{{(10 + 7)}^{2} + {(8 - (- 13))}^{2}}$

Add $10$ and $7$ .

$\sqrt{17^{2} + {(8 - (- 13))}^{2}}$

Raise $17$ to the power of $2$ .

$\sqrt{289 + {(8 - (- 13))}^{2}}$

Multiply $- 1$ by $- 13$ .

$\sqrt{289 + {(8 + 13)}^{2}}$

Add $8$ and $13$ .

$\sqrt{289 + 21^{2}}$

Raise $21$ to the power of $2$ .

$\sqrt{289 + 441}$

Add $289$ and $441$ .

$\sqrt{730}$

The result can be shown in multiple forms.

Exact Form:

$\sqrt{730}$

Decimal Form:

$27.01851217 \dots$