Find the Distance Between Two Points (-3,-11) and (8,-42)

$(- 3, - 11)$ and $(8, - 42)$

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.

$\sqrt{{(8 - (- 3))}^{2} + {((- 42) - (- 11))}^{2}}$

Simplify.

Multiply $- 1$ by $- 3$ .

$\sqrt{{(8 + 3)}^{2} + {((- 42) - (- 11))}^{2}}$

Add $8$ and $3$ .

$\sqrt{11^{2} + {((- 42) - (- 11))}^{2}}$

Raise $11$ to the power of $2$ .

$\sqrt{121 + {((- 42) - (- 11))}^{2}}$

Multiply $- 1$ by $- 11$ .

$\sqrt{121 + {(- 42 + 11)}^{2}}$

Add $- 42$ and $11$ .

$\sqrt{121 + {(- 31)}^{2}}$

Raise $- 31$ to the power of $2$ .

$\sqrt{121 + 961}$

Add $121$ and $961$ .

$\sqrt{1082}$

The result can be shown in multiple forms.

Exact Form:

$\sqrt{1082}$

Decimal Form:

$32.89376840 \dots$