Find the Distance Between Two Points (-11,10) , (1,-8)

$(- 11, 10)$ , $(1, - 8)$

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.

$\sqrt{{(1 - (- 11))}^{2} + {((- 8) - 10)}^{2}}$

Step 3

Simplify.

Multiply $- 1$ by $- 11$ .

$\sqrt{{(1 + 11)}^{2} + {((- 8) - 10)}^{2}}$

Add $1$ and $11$ .

$\sqrt{12^{2} + {((- 8) - 10)}^{2}}$

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

$\sqrt{144 + {((- 8) - 10)}^{2}}$

Subtract $10$ from $- 8$ .

$\sqrt{144 + {(- 18)}^{2}}$

Raise $- 18$ to the power of $2$ .

$\sqrt{144 + 324}$

Add $144$ and $324$ .

$\sqrt{468}$

Rewrite $468$ as $6^{2} \cdot 13$ .

Factor $36$ out of $468$ .

$\sqrt{36 (13)}$

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

$\sqrt{6^{2} \cdot 13}$

Pull terms out from under the radical.

$6 \sqrt{13}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$6 \sqrt{13}$

Decimal Form:

$21.63330765 \dots$

Step 5