Find the Distance Between Two Points (5,-5) and (8,-8)

$(5, - 5)$ and $(8, - 8)$

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.

$\sqrt{{(8 - 5)}^{2} + {((- 8) - (- 5))}^{2}}$

Step 3

Simplify.

Subtract $5$ from $8$ .

$\sqrt{3^{2} + {((- 8) - (- 5))}^{2}}$

Raise $3$ to the power of $2$ .

$\sqrt{9 + {((- 8) - (- 5))}^{2}}$

Multiply $- 1$ by $- 5$ .

$\sqrt{9 + {(- 8 + 5)}^{2}}$

Add $- 8$ and $5$ .

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

Raise $- 3$ to the power of $2$ .

$\sqrt{9 + 9}$

Add $9$ and $9$ .

$\sqrt{18}$

Rewrite $18$ as $3^{2} \cdot 2$ .

Factor $9$ out of $18$ .

$\sqrt{9 (2)}$

Rewrite $9$ as $3^{2}$ .

$\sqrt{3^{2} \cdot 2}$

Pull terms out from under the radical.

$3 \sqrt{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt{2}$

Decimal Form:

$4.24264068 \dots$

Step 5