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

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

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.

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

Step 3

Simplify.

Subtract $9$ from $- 5$ .

$\sqrt{{(- 14)}^{2} + {(9 - (- 9))}^{2}}$

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

$\sqrt{196 + {(9 - (- 9))}^{2}}$

Multiply $- 1$ by $- 9$ .

$\sqrt{196 + {(9 + 9)}^{2}}$

Add $9$ and $9$ .

$\sqrt{196 + 18^{2}}$

Raise $18$ to the power of $2$ .

$\sqrt{196 + 324}$

Add $196$ and $324$ .

$\sqrt{520}$

Rewrite $520$ as $2^{2} \cdot 130$ .

Factor $4$ out of $520$ .

$\sqrt{4 (130)}$

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

$\sqrt{2^{2} \cdot 130}$

Pull terms out from under the radical.

$2 \sqrt{130}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{130}$

Decimal Form:

$22.80350850 \dots$

Step 5