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

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

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.

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

Simplify.

Multiply $- 1$ by $- 3$ .

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

Add $4$ and $3$ .

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

Raise $7$ to the power of $2$ .

$\sqrt{49 + {(3 - (- 4))}^{2}}$

Multiply $- 1$ by $- 4$ .

$\sqrt{49 + {(3 + 4)}^{2}}$

Add $3$ and $4$ .

$\sqrt{49 + 7^{2}}$

Raise $7$ to the power of $2$ .

$\sqrt{49 + 49}$

Add $49$ and $49$ .

$\sqrt{98}$

Rewrite $98$ as $7^{2} \cdot 2$ .

Factor $49$ out of $98$ .

$\sqrt{49 (2)}$

Rewrite $49$ as $7^{2}$ .

$\sqrt{7^{2} \cdot 2}$

Pull terms out from under the radical.

$7 \sqrt{2}$

The result can be shown in multiple forms.

Exact Form:

$7 \sqrt{2}$

Decimal Form:

$9.89949493 \dots$