Find the Distance Between Two Points (-7,4) , (-3,2)

$(- 7, 4)$ , $(- 3, 2)$

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.

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

Simplify.

Multiply $- 1$ by $- 7$ .

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

Add $- 3$ and $7$ .

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

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

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

Subtract $4$ from $2$ .

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

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

$\sqrt{16 + 4}$

Add $16$ and $4$ .

$\sqrt{20}$

Rewrite $20$ as $2^{2} \cdot 5$ .

Factor $4$ out of $20$ .

$\sqrt{4 (5)}$

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

$\sqrt{2^{2} \cdot 5}$

Pull terms out from under the radical.

$2 \sqrt{5}$

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{5}$

Decimal Form:

$4.47213595 \dots$