Find the Distance Between Two Points (-1,-7) , (5,5)

$(- 1, - 7)$ , $(5, 5)$

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.

$\sqrt{{(5 - (- 1))}^{2} + {(5 - (- 7))}^{2}}$

Step 3

Simplify.

Multiply $- 1$ by $- 1$ .

$\sqrt{{(5 + 1)}^{2} + {(5 - (- 7))}^{2}}$

Add $5$ and $1$ .

$\sqrt{6^{2} + {(5 - (- 7))}^{2}}$

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

$\sqrt{36 + {(5 - (- 7))}^{2}}$

Multiply $- 1$ by $- 7$ .

$\sqrt{36 + {(5 + 7)}^{2}}$

Add $5$ and $7$ .

$\sqrt{36 + 12^{2}}$

Raise $12$ to the power of $2$ .

$\sqrt{36 + 144}$

Add $36$ and $144$ .

$\sqrt{180}$

Rewrite $180$ as $6^{2} \cdot 5$ .

Factor $36$ out of $180$ .

$\sqrt{36 (5)}$

Rewrite $36$ as $6^{2}$ .

$\sqrt{6^{2} \cdot 5}$

Pull terms out from under the radical.

$6 \sqrt{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$6 \sqrt{5}$

Decimal Form:

$13.41640786 \dots$

Step 5