Find the Distance Between Two Points (9,3) and (5,-3)

$(9, 3)$ and $(5, - 3)$

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.

$\sqrt{{(5 - 9)}^{2} + {((- 3) - 3)}^{2}}$

Simplify.

Subtract $9$ from $5$ .

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

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

$\sqrt{16 + {((- 3) - 3)}^{2}}$

Subtract $3$ from $- 3$ .

$\sqrt{16 + {(- 6)}^{2}}$

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

$\sqrt{16 + 36}$

Add $16$ and $36$ .

$\sqrt{52}$

Rewrite $52$ as $2^{2} \cdot 13$ .

Factor $4$ out of $52$ .

$\sqrt{4 (13)}$

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

$\sqrt{2^{2} \cdot 13}$

Pull terms out from under the radical.

$2 \sqrt{13}$

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{13}$

Decimal Form:

$7.21110255 \dots$