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

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

Step 1

Use the distance formula to determine the distance between the two points.

$Distance = \sqrt{{(x_{2} - x_{1})}^{2} + {(y_{2} - y_{1})}^{2}}$

Step 2

Substitute the actual values of the points into the distance formula.

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

Step 3

Simplify.

Multiply $- 1$ by $- 5$ .

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

Add $9$ and $5$ .

$\sqrt{14^{2} + {((- 3) - 5)}^{2}}$

Raise $14$ to the power of $2$ .

$\sqrt{196 + {((- 3) - 5)}^{2}}$

Subtract $5$ from $- 3$ .

$\sqrt{196 + {(- 8)}^{2}}$

Raise $- 8$ to the power of $2$ .

$\sqrt{196 + 64}$

Add $196$ and $64$ .

$\sqrt{260}$

Rewrite $260$ as $2^{2} \cdot 65$ .

Factor $4$ out of $260$ .

$\sqrt{4 (65)}$

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

$\sqrt{2^{2} \cdot 65}$

Pull terms out from under the radical.

$2 \sqrt{65}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{65}$

Decimal Form:

$16.12451549 \dots$

Step 5