Find the Distance Between Two Points (7,-1) and (9,-9)

$(7, - 1)$ and $(9, - 9)$

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.

$\sqrt{{(9 - 7)}^{2} + {((- 9) - (- 1))}^{2}}$

Step 3

Simplify.

Subtract $7$ from $9$ .

$\sqrt{2^{2} + {((- 9) - (- 1))}^{2}}$

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

$\sqrt{4 + {((- 9) - (- 1))}^{2}}$

Multiply $- 1$ by $- 1$ .

$\sqrt{4 + {(- 9 + 1)}^{2}}$

Add $- 9$ and $1$ .

$\sqrt{4 + {(- 8)}^{2}}$

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

$\sqrt{4 + 64}$

Add $4$ and $64$ .

$\sqrt{68}$

Rewrite $68$ as $2^{2} \cdot 17$ .

Factor $4$ out of $68$ .

$\sqrt{4 (17)}$

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

$\sqrt{2^{2} \cdot 17}$

Pull terms out from under the radical.

$2 \sqrt{17}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{17}$

Decimal Form:

$8.24621125 \dots$

Step 5