Find the Distance Between Two Points (-6,-1) , (6,3)

$(- 6, - 1)$ , $(6, 3)$

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.

$\sqrt{{(6 - (- 6))}^{2} + {(3 - (- 1))}^{2}}$

Step 3

Simplify.

Multiply $- 1$ by $- 6$ .

$\sqrt{{(6 + 6)}^{2} + {(3 - (- 1))}^{2}}$

Add $6$ and $6$ .

$\sqrt{12^{2} + {(3 - (- 1))}^{2}}$

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

$\sqrt{144 + {(3 - (- 1))}^{2}}$

Multiply $- 1$ by $- 1$ .

$\sqrt{144 + {(3 + 1)}^{2}}$

Add $3$ and $1$ .

$\sqrt{144 + 4^{2}}$

Raise $4$ to the power of $2$ .

$\sqrt{144 + 16}$

Add $144$ and $16$ .

$\sqrt{160}$

Rewrite $160$ as $4^{2} \cdot 10$ .

Factor $16$ out of $160$ .

$\sqrt{16 (10)}$

Rewrite $16$ as $4^{2}$ .

$\sqrt{4^{2} \cdot 10}$

Pull terms out from under the radical.

$4 \sqrt{10}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$4 \sqrt{10}$

Decimal Form:

$12.64911064 \dots$

Step 5