Find the Distance Between Two Points (-3,5) and (7,-1)

$(- 3, 5)$ and $(7, - 1)$

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.

$\sqrt{{(7 - (- 3))}^{2} + {((- 1) - 5)}^{2}}$

Simplify.

Multiply $- 1$ by $- 3$ .

$\sqrt{{(7 + 3)}^{2} + {((- 1) - 5)}^{2}}$

Add $7$ and $3$ .

$\sqrt{10^{2} + {((- 1) - 5)}^{2}}$

Raise $10$ to the power of $2$ .

$\sqrt{100 + {((- 1) - 5)}^{2}}$

Subtract $5$ from $- 1$ .

$\sqrt{100 + {(- 6)}^{2}}$

Raise $- 6$ to the power of $2$ .

$\sqrt{100 + 36}$

Add $100$ and $36$ .

$\sqrt{136}$

Rewrite $136$ as $2^{2} \cdot 34$ .

Factor $4$ out of $136$ .

$\sqrt{4 (34)}$

Rewrite $4$ as $2^{2}$ .

$\sqrt{2^{2} \cdot 34}$

Pull terms out from under the radical.

$2 \sqrt{34}$

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{34}$

Decimal Form:

$11.66190378 \dots$