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

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

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.

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

Step 3

Simplify.

Multiply $- 1$ by $- 7$ .

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

Add $- 5$ and $7$ .

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

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

$\sqrt{4 + {(7 - 1)}^{2}}$

Subtract $1$ from $7$ .

$\sqrt{4 + 6^{2}}$

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

$\sqrt{4 + 36}$

Add $4$ and $36$ .

$\sqrt{40}$

Rewrite $40$ as $2^{2} \cdot 10$ .

Factor $4$ out of $40$ .

$\sqrt{4 (10)}$

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

$\sqrt{2^{2} \cdot 10}$

Pull terms out from under the radical.

$2 \sqrt{10}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{10}$

Decimal Form:

$6.32455532 \dots$

Step 5