Find the Distance Between Two Points (-6,-5) , (6,10)

$(- 6, - 5)$ , $(6, 10)$

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.

$\sqrt{{(6 - (- 6))}^{2} + {(10 - (- 5))}^{2}}$

Step 3

Simplify.

Multiply $- 1$ by $- 6$ .

$\sqrt{{(6 + 6)}^{2} + {(10 - (- 5))}^{2}}$

Add $6$ and $6$ .

$\sqrt{12^{2} + {(10 - (- 5))}^{2}}$

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

$\sqrt{144 + {(10 - (- 5))}^{2}}$

Multiply $- 1$ by $- 5$ .

$\sqrt{144 + {(10 + 5)}^{2}}$

Add $10$ and $5$ .

$\sqrt{144 + 15^{2}}$

Raise $15$ to the power of $2$ .

$\sqrt{144 + 225}$

Add $144$ and $225$ .

$\sqrt{369}$

Rewrite $369$ as $3^{2} \cdot 41$ .

Factor $9$ out of $369$ .

$\sqrt{9 (41)}$

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

$\sqrt{3^{2} \cdot 41}$

Pull terms out from under the radical.

$3 \sqrt{41}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt{41}$

Decimal Form:

$19.20937271 \dots$

Step 5