Find the Distance Between Two Points (-6,1) , (5,-1)

$(- 6, 1)$ , $(5, - 1)$

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.

$\sqrt{{(5 - (- 6))}^{2} + {((- 1) - 1)}^{2}}$

Step 3

Simplify.

Multiply $- 1$ by $- 6$ .

$\sqrt{{(5 + 6)}^{2} + {((- 1) - 1)}^{2}}$

Add $5$ and $6$ .

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

Raise $11$ to the power of $2$ .

$\sqrt{121 + {((- 1) - 1)}^{2}}$

Subtract $1$ from $- 1$ .

$\sqrt{121 + {(- 2)}^{2}}$

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

$\sqrt{121 + 4}$

Add $121$ and $4$ .

$\sqrt{125}$

Rewrite $125$ as $5^{2} \cdot 5$ .

Factor $25$ out of $125$ .

$\sqrt{25 (5)}$

Rewrite $25$ as $5^{2}$ .

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

Pull terms out from under the radical.

$5 \sqrt{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$5 \sqrt{5}$

Decimal Form:

$11.18033988 \dots$

Step 5